1)737'%0) (=2%1-'7 %2( &392(%6= 0%=)6 03; 0):)0...

1)737'%0)�(=2%1-'7�%2(�&392(%6=�0%=)67869'896)�-2�8343+6%4,-'%00=�*36')(

03;�0):)0�.)87

78)*%2�7Ó()6&)6+

(ITEVXQIRX�SJ�1IXISVSPSK]7XSGOLSPQ�9RMZIVWMX]

7XSGOLSPQ��

Doctoral dissertation 2004-03-26Department of MeteorologyStockholm UniversitySE-106 91 STOCKHOLM, Sweden

ABSTRACT

Two types of mesoscale wind-speed jet and their effects on boundary-layer structure werestudied. The first is a coastal jet off the northern California coast, and the second is akatabatic jet over Vatnajökull , Iceland. Coastal regions are highly populated, and studies ofcoastal meteorology are of general interest for environmental protection, fishing industry,and for air and sea transportation. Not so many people live in direct contact with glaciers butproperties of katabatic flows are important for understanding glacier response to climaticchanges. Hence, the two jets can potentially influence a vast number of people.

Flow response to terrain forcing, transient behavior in time and space, and adherence tosimplified theoretical models were examined. The turbulence structure in these stablystratified boundary layers was also investigated. Numerical modeling is the main tool in thisthesis; observations are used primaril y to ensure a realistic model behavior.

Simple shallow-water theory provides a useful framework for analyzing high-velocity flowsalong mountainous coastlines, but for an unexpected reason. Waves are trapped in theinversion by the curvature of the wind-speed profile, rather than by an infinite stabil ity inthe inversion separating two neutral layers, as assumed in the theory. In the absence ofblocking terrain, observations of steady-state supercritical flows are not likely, due to thediurnal variation of flow criticali ty.

In many simplified models, non-local processes are neglected. In the flows studied here, weshowed that this is not always a valid approximation. Discrepancies between simulatedkatabatic flow and that predicted by an analytical model are hypothesized to be due to non-local effects, such as surface inhomogeneity and slope geometry, neglected in the theory. Ona different scale, a reason for variations in the shape of local similarity scaling functionsbetween studies is suggested to be differences in non-local contributions to the velocityvariance budgets.

Stefan SöderbergISBN 91-7265-812-6, pp 1-45.Printed by PrintCenter, Stockholm University, Stockholm, Sweden, 2004.

List of papersThis thesis consists of the present summary and the following papers. In thesummary, the papers are referred to by their Roman numerals.

SUPERCRITICAL CHANNEL FLOW IN THE COASTAL ATMOSPHERIC BOUNDARY LAYER:IDEALIZED NUMERICAL SIMULATIONS.

S. Söderberg, and M. Tjernström

Journal of Geophysical Research, 106, 17811-17829, 2001.

DIURNAL CYCLE OF SUPERCRITICAL

ALONG-COAST FLOWS.

S. Söderberg, and M. Tjernström

Journal of the Atmospheric Sciences, 59, 2615-2624, 2002.

THE TURBULENCE STRUCTURE OF THE STABLE ATMOSPHERIC BOUNDARY LAYER

AROUND A COASTAL HEADLAND: AIRCRAFT OBSERVATIONS AND MODELLING RESULTS.

I. M. Brooks, S. Söderberg, and M. Tjernström

Boundary-Layer Meteorology, 107, 531–559, 2003.

NUMERICAL SIMULATIONS AND ANALYTICAL ESTIMATES OF KATABATIC FLOW OVER A

MELTING OUTFLOW GLACIER.

S. Söderberg, and O. Parmhed

Submitted to Boundary-Layer Meteorology, 2004.

The idea for Paper I was proposed by the second author. I set up and performed thenumerical experiments, and analyzed the model results. The text was jointly writtenwith the co-author; I wrote approximately 75% of the paper, including most of thetext describing the model results, the discussion, and the summary. The idea forPaper II was jointly discussed with the co-author, while I set up the numericalexperiments, analyzed the results and wrote most of the text. In Paper III , mycontribution was to set up and perform the model experiment. I also performed theinitial analysis of the model results and contributed with parts of the text, related tothe model set up and model results. The first author put all the text together into itsfinal form. In Paper IV, I was responsible for the model set up, the analysis of allthe model results and the related text, and wrote most of the discussion. Additionalpreliminary material, concerning the turbulence structure of a boundary layerdominated by a katabatic wind-speed jet, is included in the summary (see section 5).For these results, I am solely responsible.

IV

III

II

I

Contents

1. Introduction 31.1 Motivation 41.2 General considerations 5

2. Tools used in the study 72.1 Measurements 72.2 Numerical models 8

2.1.1 MIUU Model 82.1.2 COAMPSTM 8

3. Background and internal flow dynamics inlow-level jets 93.1 The coastal jet 9

3.1.1 Mean MABL structure 93.1.2 Adjustment of the MABL to the coastline

geometry 113.1.3 Transient behavior of supercritical MABL

flows 183.2 The katabatic jet 20

4. Boundary-layer characteristics in thepresence of low-level jets 25

5. Turbulence structure in stable boundarylayers 28

6. Concluding remarks and future outlook 39

Acknowledgements 41

References 42

TOPOGRAPHICALLY FORCED LOW-LEVEL JETS

3

1. Introduction

In the atmosphere, wind-speed jets exist on many scales, both in time and space. Twoexamples are the nocturnal boundary-layer jet, and the midlatitude jet streams. The former isan inertial oscill ation of the wind, typicall y found a few hundred meters above ground andinitiated close to sunset. Super-geostrophic magnitudes of the wind speed are due to therapid reduction of turbulence and the associated momentum flux during the eveningtransition, causing an imbalance of forces. The latter jet is geostrophically balanced, and aresult of temperature differences between different air masses, as part of the generalcirculation of the atmosphere. Wind speeds of as much as 75 ms -1 are quite typical in the jetcore, which is found at around 10 km height.

In the present thesis we will focus on two other types of jet, both dependent on horizontaltemperature differences in the atmosphere. The first is a coastal jet driven by cross-coastbaroclinicity, which arises from the differential heating of land and sea. The geographicalarea in focus in these studies is the west coast of the United States (Figure 1). The secondtype is a katabatic jet over a melting glacier. This jet is driven by negative buoyancy, whichacts also in the horizontal due to a temperature difference between the surface and the air atthe same height above sea level, but away from the surface. To study the katabatic jet, weturn to Breidamerkurjökull , an outlet glacier - part of the Vatnajökull i cecap in Iceland(Figure 2).

While coastal jets are strongly influenced by complex coastal terrain features such as capes,but not dependent on them for their existence, a sloping terrain is necessary for theformation of katabatic jets. The adjustment of boundary-layer flows to complex terrain istherefore one of the issues inherently included in this thesis. Another issue explored here isthe turbulence structure of the stably stratified boundary layer in which these wind-speedjets exist.

Both observations and numerical simulations are part of the study. The observations havebeen used mainly to verify that the numerical models are capable of simulating the physicalproperties and processes within the studied flows, and to ensure a realistic behavior of themodel results. Hence, although numerical modeling has been the main tool, observationsconstitute one of the fundaments on which the conclusions in this thesis rely. The presentexecutive summary largely consists of findings from Papers I-IV; however, additionalpreliminary material is included in section 5 to broaden the picture. Some of the questionsaddressed in the thesis are:

• Is hydraulic theory a valid analog for describing high-velocity flows along mountainouscoastlines, even though results have cast doubts on its applicabili ty? (Papers I and II)

• How well can an analytical model predict katabatic flow characteristics from simulatedbackground parameters? (Paper IV)

• Can a physical explanation be found for the differences in the form of the local similarityscaling functions between several studies? (Paper III and preliminary material)

STEFAN SÖDERBERG

4

1.1 Motivation

A classical approach in atmospheric studies is to divide the atmosphere into a number ofspheres. The lowest sphere, approximately 10 km deep, is called the troposphere andconstitutes the larger part of the atmospheric mass. The troposphere is in turn divided into aturbulent boundary layer, separated from the free atmosphere above, often by an inversion;there is a large contrast between the two layers in terms of temperature, wind speed, andhumidity. The boundary layer is here the part of the atmosphere, which is directlyinfluenced by Earth's surface and where all energy input by the sun finally is dissipated toheat. The atmospheric boundary layer is also the part of the atmosphere where most peoplespend most of their time. Still , our current knowledge about the boundary layer, for examplethe stably stratified boundary layer, is to some extent inadequate. Although these facts inthemselves motivate studies of the atmospheric boundary layer in general, additionalarguments for studying coastal jets and katabatic flows in particular, are given below.

A reason for studies of coastal meteorology in general, is that a large part of the Earth'spopulation lives in coastal areas. Typical coastal phenomena, such as sea breezes, may be ofgreat importance for environmental protection in certain areas. Shipping activities and airtraffic at coastal airports are also severely limited by rapid transitions from clear to foggyconditions, typical for many coastal regions.

Interest in the persistent northerly or northwesterly boundary layer flow along much of theU.S. west coast in late spring through early fall , was initiated partly because of its effect onoceanic upwell ing. Along the entire coast, surface waters are forced to flow offshore and isreplaced by cold and nutrient rich water from below, a process driven by Ekman pumping.In regions along the coast where high wind-speeds frequently are observed, in particular

−135 −130 −125 −120 −115

25

30

35

40

45

50

Longitude

Latit

ude

HL

Cape Blanco

Cape Mendocino

Point SurPoint Conception

San Fransisco

Los Angeles

Figure 1. Map over the U.S. west coast, H and L indicate approximate summertime positions of the NorthPacific High and a continental thermal low, respectively. Terrain elevation greater than 400 m is shaded. Thearrows indicate the prevaili ng wind directions along the coast.


5

downstream of capes and headlands, a close correlation between the spatial distribution ofthe surface wind stress and that of the coldest sea surface temperatures (SSTs) are found(e.g., Beardsley et al. 1987; Rogers et al. 1998; Dorman et al. 2000). Thus, there is a directeconomic interest in increasing the knowledge about this coastal boundary-layer flow,maybe not so much for increasing the number of sunbathing tourists in coastal resorts, as forthe fishing industry.

In contrast to coastal areas, not so many people live in direct contact with glaciers.Nevertheless, the current interest in climate change and related issues such as glaciermelting and sea-level rise, have highlighted the need for a better understanding of the massbalance of ice caps. During summer, stable boundary layers are often formed over meltingglaciers and as pointed out by many authors, stable boundary layer are still poorlyunderstood and not well described in numerical weather and climate models (e.g., Poulos etal. 2002). Moreover, over sloping melting glaciers, katabatic flows are frequently found, anddrive a turbulent exchange of heat and momentum between the surface and the freeatmosphere. Since glacier melting is most sensitive to changes in long-wave radiation andturbulent heat flux (e.g., Oerlemans 2001), the properties of katabatic flows are importantfor the understanding of glacier response to climatic changes. In addition, katabatic flowscan form over cool sloping surfaces in general and thus can be of importance for the surfaceenergy budgets in areas where stable boundary layers forms over land, on a regular basis.

1.2 General considerations

Important to note already here is that in atmospheric sciences, a “wind jet” typically standsfor a wind-speed maximum in the vertical, regardless of cross-flow dimensions, and not anossle jet like in classical fluid dynamics. This has some implications for the aspect ratios ofthe studied jets as will be discussed later. First a few comments on the range of scales of

−30 −25 −20 −15 −10 −5 60

61

62

63

64

65

66

67

68

69

Latit

ude

Longitude

Vatnajökull

Grid 1∆x = 27 km43x34x40

Grid 2∆x = 9 km88x70x40

Grid 3∆x = 3 km91x85x40

(a)

−18 −17 −16 −15 −14 −13

63

63.5

64

64.5

65

Longitude

Latit

ude

500

500

10001000

10001500

1500

Breidamerkurjökull

(b)

Figure 2. Horizontal model domains for the real-data COAMPS case study in Paper IV and for theadditional material included in section 5. Terrain elevation is contoured every 250 m, black bold lines is thecoastline: (a) Coarse mesh (grid 1) and the two inner nests (grid 2 and 3), gray bold lines indicate outer rimof each grid; (b) The innermost nest (grid 3) with a horizontal resolution of 3 km.

STEFAN SÖDERBERG

6

atmospheric motions and surface characteristics influencing the studied wind-speed jets aregiven.

The background marine atmospheric boundary layer (MABL) flow condition, in which thecoastal jet exists, is synoptically determined. The MABL flow, roughly within a Rossbyradius of deformation (~50-100 km), then adjusts to capes and points, and gaps in thecoastal mountain ridge (Papers I and II) . These coastal terrain features typically have ahorizontal scale of the order of ~10-50 km. SST variations due to oceanic upwell ing arefound along most of the U.S. west coast. Within a few kilometers, the SST can vary severaldegrees. This can lead to the formation of internal stable boundary layers, which influencethe MABL turbulence structure (Paper III ).

As will be discussed in Paper IV, katabatic jets over melting glaciers appear to be relativelyinsensitive to motions on the synoptic scale. Instead, the length and width of the glacier setthe upper limit of the horizontal scale affecting the flow. In the present thesis, the length ofthe glacier is of the order of ~20 km while the width is of the order of ~10 km. However,note that katabatic jets in principle have no cross-flow limits other than the width of theslope.

The coastal jet has a wind-speed maximum with vertical extent of the order of ~100 m,while the cross-flow width of the jet core is ~20-50 km. Although the katabatic layer ismuch shallower with a wind-speed maximum typically found ~10-20 m above the glaciersurface, the width of Breidamerkurjökull results in aspect ratios of the order of ~10-3 forboth the coastal and the katabatic jet. However, the glacier is anything but smooth andsurface roughness elements of the order of ~1 m are common. Features on that scale are notresolved in the numerical simulations performed here, but certainly have an effect on theobserved turbulence structure, since wake turbulence is likely to be found in the immediatesurroundings of these obstacles. Moreover, surface roughness elements with a size of ~1 m,corresponding to 5-10% of the jet height, will affect also the observed mean verticalstructure. The ocean surface on the other hand is smooth. However, obstacles in the form ofcapes, force the boundary-layer flow to either go around, or cross the obstacle. In fact, thevertical extent of the local terrain at Cape Mendocino (see Figure 1) corresponds to morethan half of the typical MABL depth upwind of the cape. Instead of wake turbulence, as inthe katabatic flow, this obstacle triggers a lee-wave, which in some cases may break.

Considering time scales, the coastal jet found along the northern California coast and thekatabatic flow over Vatnajökull, are mainly summertime phenomena. Observations haveshown that they are persistent features interrupted only for short periods of time. While thestrength of the coastal jet varies with the diurnal cycle (Paper II), the katabatic jet shows noclear diurnal cycle. This is because the temperature of the coastal landmass varies with solarinsolation, while the glacier surface temperature is typically constant at its melting point(Paper IV).

Stratiform clouds are common in the two geographical areas in focus here (e.g., Brost et al.1982; Kaltenböck and Obleitner 1999), and are certainly important for the radiation balanceof the atmosphere and the underlying surfaces. Possible effects of clouds on the jets are notcovered in the present thesis for the reasons given below. Marine stratocumulus within the


7

MABL can affect the strength of the inversion through radiational cooling at the cloud top.However, the coastal jet is mainly driven by a thermal wind caused by the slope of theinversion towards the coast, rather than by the strength of the inversion. Moreover, thebackground conditions used in the simulations in Papers I-III were in fact based on a cloudfree day. The glacier surface temperature, which largely controls the strength of thekatabatic flow, is during summertime limited on the high side by the melting point of snowand ice; this is typically below the ambient atmospheric temperature. Thus, it is not likelythat the clouds through their effect on the radiational balance at the surface have a directinfluence on the katabatic flow studied in Paper IV, although clouds certainly have an effecton the rate of the glacier melting itself.

Another feature that lies outside the scope of this thesis is what is usually referred to as acoastally trapped disturbance or wind reversal. Several times each summer, the persistentnortherly or northwesterly MABL flow off the U.S. west coast is interrupted by a period ofsoutherly winds, caused by a northward propagating disturbance in the MABL. Thisdisturbance has in the literature been described as a Kelvin wave (Dorman 1988), internalbore (Klemp et al. 1997), or a mixed Kelvin wave-bore (Ralph et al. 2000). An overview ofthe different views is given by Nuss et al. (2000).

2. Tools used in the study

2.1 Measurements

Although detailed analyses of observational data have not been part of the author's workthey constitute a basis for this thesis. Observational data have been used to verify a realisticbehavior of the numerical models employed and to verify that they are capable of simulatingthe physical processes important in the flows. When the general characteristics of thesimulated flow correspond to observations, the model results can be a good help inunderstanding physical processes behind features we are observing. Moreover, numericalsimulations can give vital information on what should be monitored, the next time a fieldexperiment is planned.

The observational data used in the present thesis have been collected from two fieldexperiments. The Coastal Waves 1996 experiment was set up to map the MABL structureoff the California coast in summer conditions. The primary measurement platform was theNational Center for Atmospheric Research C-130 Hercules aircraft. Several instrumentedsites were also deployed along the Cali fornia coast. Among the questions addressed in theexperiment, were the supercriticali ty and the turbulence structure of the MABL. Details canbe found in Rogers et al. (1998).

The main goal of the 1996 glacio-meteorological field experiment on Vatnajökull, Iceland,was to understand how the energy used in the melting of snow and ice is transferred to thesurface. Several meteorological stations were operated both on and off the ice cap. Aconcentration of stations was put on Breidamerkurjökull , an outlet glacier flowing down tothe Atlantic Ocean. To obtain vertical profiles of the boundary layer, a tethered balloon andradiosonds were used. An overview of the experiment is given by Oerlemans et al. (1999).

STEFAN SÖDERBERG

8

2.2 Numerical models

Two different numerical models have been used in the present thesis. In Papers I-III theDepartment of Meteorology Uppsala University (MIUU) mesoscale model was applied tothe coastal jet along the northern Cali fornia coast. In two preceding studies the same modelwas successfully applied to this area and we therefore chose to use the same tool to answerthe scientific questions posed in Papers I-III . The model utili zed in Paper IV is the CoupledOcean/Atmosphere Mesoscale Prediction System (COAMPSTM) version 2.0 atmosphericmodel (Hodur 1997).

2.1.1 MIUU Model

The MIUU mesoscale model is a hydrostatic non-linear primitive equations model. Thevertical coordinate is transformed to a terrain-following sigma-z vertical coordinate system.To achieve high resolution in the center of the model and locate the lateral boundaries farfrom the area of interest, a horizontally expanding grid can be used. The vertical grid isexpanding, log-linearly, towards the model top. The turbulence closure is a modified“Level-2.5” closure (Mellor and Yamada 1982), including a correction for non-realizablesecond-order moments, inherent in this type of closure, and an improved formulation for thepressure redistribution terms in the turbulent kinetic energy (TKE) equation, the “wallcorrection” (Andrén 1990). The model allows for an easy experimental control over thesurface forcing and initial conditions, facil itating both analyses of model results andsensitivity tests. The MIUU model has been used in a variety of applications, including oro-graphic (e.g., Enger and Grisogono 1998) and coastal flows (e.g., Tjernström and Grisogono2000). More detailed descriptions are found in Tjernström (1987a, b) and Enger (1990).

2.1.2 COAMPSTM

The Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPSTM) version 2.0atmospheric model, developed at the U.S. Naval Research Lab, Monterey, CA, is anonhydrostatic compressible model, with terrain-following sigma-z vertical coordinatesystem. Nested grids can be used in idealized and real-case simulations allowing highhorizontal resolution for a given area. Physical parameterization schemes include long- andshortwave radiation (Harshvardan et al. 1987), explicit moist physics (Rutledge and Hobbs1983), cumulus convection (Kain and Fritsch 1990), and “Level-2.5” turbulence closure(Mellor and Yamada 1982). The ground surface temperature is computed using a surfaceenergy balance scheme. Initial and lateral boundary conditions were provided usingECMWF analyses in the real-case study. This allows us to compare the simulated katabaticflow in realistic atmospheric conditions to measurements undertaken during the fieldexperiment on Vatnajökull described above. A more complete model description is found inHodur (1997).


9

3. Background and internal flow dynamics in low-level jets

Low-level jets are by definition found close to the ground and therefore directly influencedby the surface properties. In fact, some low-level jets are even formed due to suddenchanges in surface properties. An example of this is the frequently observed low-level jetover the Baltic Sea (e.g., Smedman et al. 1995). When warm air from land is advected overthe cold sea, this result in a frictional decoupling and the formation of an inertial oscillationdue to an imbalance of forces - a spatial analog to the nocturnal jet briefly described in theintroduction. Below the jet-types specifically studied in this thesis are presented in moredetail , namely coastal jets established along coastlines with elevated terrain and katabaticjets formed over melting glaciers.

3.1 The coastal jet

3.1.1 Mean MABL structure

In late spring through early fall , the near-surface air flow over the eastern North Pacific isdominated by the North Pacific high, located ≈ 1000 km west of the California coast near40° north, and a thermal low over the southwestern U.S. continent (Figure 1). Thesesynoptic-scale features set the stage for persistent northerly or northwesterly boundary-layerflow along much of the U.S. west coast. The MABL is typically cool, moist and well mixedby turbulence; the air temperature is largely controlled by the SST with colder SSTs closerto the coast than offshore due to upwell ing. A strong temperature inversion, typically of theorder of 10 °C in potential temperature, forms a boundary between the MABL and thesubsiding dry and warm air in the free atmosphere above. Due to the decreasing MABLtemperature towards the coast, the inversion slopes gently from west to east. Close to thecoast, the slope of the inversion increases significantly since the land surface is usuallywarmer than the air within the MABL. A typical near-shore MABL depth is 200-300 mwhile the height of the coastal terrain for much of the U.S. west coast exceeds 400 m (seeFigure 1). The inversion will therefore intersect the coastal mountain range, which acts as abarrier to the flow. This means that air with an initial component of motion toward thebarrier eventually must turn and flow along the barrier; thus the MABL flow is channeled.In general, even moderate terrain can block onshore flow if it is hydrodynamically steep(Grisogono and Tjernström 1996; Tjernström and Grisogono 1996).

Although the channeling of the flow by itself can lead to the formation of coastal jets, themain contributor to the acceleration of the near-shore flow along straight sections of theU.S. west coast is a thermal wind. The thermal wind is a result of the sloping inversion,which give rise to a horizontal temperature gradient directed towards the coast. Anapproximate form of the thermal wind can be written as (e.g., Stull 1988):

y

T

fT

g

z

ug

∂∂−≈

∂∂

, (1)

x

T

fT

g

z

vg

∂∂+≈

∂∂

, (2)

STEFAN SÖDERBERG

10

where ug and vg are the geostrophic wind components, g is gravitational acceleration, f is theCoriolis parameter, and T is temperature. Here u, v, x, y, and z have their usual definition; uis parallel to the x-axis (directed towards east), v is parallel to the y-axis (directed towardsnorth), and z is the vertical axis. A sloping inversion towards the coast like off the U.S. westcoast will give a positive RHS in (2). Taking a finite difference over a layer ∆z thereforeyields:

0>− L,gU,g vv. (3)

Here U stands for the upper level and L for the lower level. In a northerly flow, (3) impliesthat vg,L must be more negative than vg,U, i.e., a stronger northerly flow at the lower level.Thus, off the U.S. west coast the thermal wind gives rise to an increasing wind speed withdecreasing height. Within the MABL the effect of surface friction also comes into play,which leads to a jet shaped wind profile with a wind-speed maximum just below theinversion. It has been suggested that a small thermal wind below the inversion, caused bythe SST gradient towards the coast, also contributes to the northerly flow (Zemba and Friehe1987). However, numerical simulations have shown that the SST distribution has onlymarginal effects on the character of the along-coast flow (Burk and Thompson 1996;Tjernström and Grisogono 2000). The above description of the MABL off the U.S. westcoast can be summarized by the conceptual model of Beardsley et al. (1987) shown inFigure 3. Stratus and fog are indicated below the inversion in the intermediate and nearshoreregions but even if marine stratocumulus and fog are common along the entire U.S. westcoast, they are not a topic studied in this thesis for reasons previously discussed. Moreover,numerical simulations have shown that the cloud field along the coast is determined almostentirely by local flow dynamics (Tjernström 1999); observations also show a preferredclearing in the lee of capes and points with prominent local terrain features (e.g., Rogers etal. 1998; Dorman et al. 2000).

Figure 3. Conceptual model of average lower atmosphere over eastern North Pacific during periods ofpersistent northerly or northwesterly winds in summer. (From “Local atmospheric forcing during the coastalocean dynamics experiment. 1. A description of the marine boundary layer and atmospheric conditions overa northern California upwelling region,” R. C. Beardsley, C. E. Dorman, C. A. Friehe, L. K. Rosenfeld, andC. D. Winant, J. Geophys. Res., 92: 1481, 1987.)


11

The momentum balance in coastal jets along the U.S. west coast has been investigated bothfrom observational data and from numerical model results by several authors (e.g., Zembaand Friehe 1987; Samelson and Lentz 1994; Ström et al. 2001; Burk et al. 1999; Tjernströmand Grisogono 2000). In strong northerly flow along straight sections of the coastline, theflow is geostrophic in the cross-coast direction, while the pressure gradient force is balancedby turbulent friction in the along-coast direction. Downstream of points and in the lee ofcapes protruding into the flow, the situation is more complex. Advection of momentumbecomes important, both in the cross-coast and along-coast momentum budgets.Furthermore, as the MABL depth decreases, friction also becomes important in the cross-coast direction; the increased effect of friction on the flow as the MABL depth decreaseswas also demonstrated in Paper I by theoretical considerations of the shallow-waterequations. Variations in the MABL connected to topographic features in the coastal terrainare not included in the conceptual model described above, since it assumes a straightcoastline with a smooth coastal range. The sensitivity of along-coast flow to terrain forcingis addressed in Paper I and discussed in the next section.

3.1.2 Adjustment of the MABL to the coastline geometry

As a consequence of the strong capping inversion above the well-mixed MABL, it has beensuggested that the dynamics of the coastal flow off the U.S. west coast can be approximatedas a single-layer reduced-gravity (shallow water) flow past a blocking sidewall (Winant etal. 1988). Hydraulic theory then predicts that the Froude number, Fr, the ratio of the flowspeed U to the linear gravity wave phase speed c of the waves propagating on the interfacebetween the MABL and the free atmosphere above, determines the behavior of the flow:

c

U=Fr , (4)

where

( ) 50.H'gc = . (5)

The depth of the layer is H and g' is the reduced gravity, here expressed using the potentialtemperature θ:

0θθ∆= g'g , (6)

where θ0 is the temperature of the lower layer and ∆θ is the temperature jump over thecapping inversion. When the flow is supercritical, Fr > 1, the flow becomes sensitive tochanges in coastline orientation (Ippen 1951). Physically supercritical flow means that themass and wind field upstream of a local perturbation cannot adjust to this, since the phasespeed of the waves responsible for the adjustment process is lower that the flow speed. Oneway to interpret this is that the information is “swept downstream” by the flow. As thevertical boundaries of the channel expand or contract, expansion fans or hydraulic jumpswill appear when the flow is supercritical. A simple sketch of a supercritical flow in awidening channel based on the theory by Ippen (1951) is shown in Figure 4. The blocking

STEFAN SÖDERBERG

12

coastline turns away from the flow at an angle α to the upstream flow direction. In responseto this the depth of the MABL decreases and the flow accelerates. An expansion fan formsdownstream of a characteristic wave, which makes an angle β1 to the upstream flow givenby:

( ) 11 Fr−=βsin , (7)

beyond which no information can propagate. As the Froude number increases downstreamof the initial characteristic, successive characteristics diverge confining the expansion fanbetween the leading wave and the trail ing wave, which makes an angle β2 to the downstreamcoastline.

If the hydraulic theory holds true for the MABL along the U.S. west coast it would be auseful analog and explain the observed “patchiness” of the low-level wind fields. High windspeeds are frequently observed downstream of capes and points and sudden decelerations ofthe flow, are also found where it encounters topographic features protruding into the flow(e.g., Dorman et al. 2000). Numerous experiments with shallow water models have beenreasonably successful in describing the main characteristics of the observed flow (e.g.,Samelson 1992; Rogerson 1999; Edwards et al. 2001). One of the main results in Samelson(1992) was the demonstration of the effect of friction. The region with increased windspeeds resembled a “bulge” rather than a fan when friction was included. Thus, the inclusionof friction in the theory led to a much better agreement between shallow-water model resultsand observed flow structures. But, reali ty is by its very nature three-dimensional andtherefore it is well motivated to test the hydraulic theory in such a model.

In Paper I the three-dimensional, hydrostatic, non-linear MIUU mesoscale model was usedin a number of sensitivity tests focusing on the effect of terrain forcing on along-coastsupercritical flow. A smooth mountain barrier was generated by fitting a simple parabolicfunction to an ensemble of east-west cross-sections of the real terrain north of CapeMendocino. A piece-wise linear convex bend in the idealized coastline was then introduced,making an angle α = 24° to the upstream coastline, similar to the real terrain south of CapeMendocino. The simplified terrain thus represents the real terrain forcing of the northern

Figure 4. Schematic sketch of supercritical channel flow based upon the theory of Ippen (1951). U is theflow velocity and H is the fluid depth. See text for a definition of the angles α, β1, and β2.


13

California coastline while ignoring small changes in coastline orientation and terrain height.By varying this terrain in a simple manner, testing of hypothesis related to coastlinegeometry was facilit ated. Three sets of tests were performed, focusing on coastline shape,terrain height variations, and the effects of a cape perpendicular to the flow, respectively.Examples of different idealized terrain configurations are shown in Figure 5. In Figure 5athe terrain used in the control run (Ctrl) is shown, 5b shows a curved coastline (z1_Cc24),5c shows a sloping coastal barrier (z4_α24), and in 5d a coastline with a cape representingthe real terrain at Cape Mendocino is shown (z1_cape500). In Paper I, all model results wereextracted at 1500 local standard time, 21 hours into the simulations; some of the results arepresented below. The flow is always from the north so upstream (downstream) means to thenorth (south) of the change in coastline orientation. Detailed descriptions of the experimentsare found in Table 1 in Paper I.

In Figure 6 the MABL depth, maximum MABL wind speed, and Fr from Ctrl are shown.Downstream of the bend in the coastline, a fan-like depression of the MABL depth extendsfrom the coast (Figure 6a). In response to the decreased MABL depth, the flow acceleratesand attains wind speeds exceeding 22 ms -1 within a bulge-like wind-speed maximum(Figure 6b). These results are basically in agreement with results from studies utili zingshallow-water models. However, even though the flow is supercritical (Figure 6c), there is agradual increase of the flow velocity along the upstream coastline. This is clearly not inagreement with the hydraulic theory described above. This unexpected feature was present

−150−100

−500

50100

150

−100−50

050

100

0

0.5

1

1.5

West

− East

(km)

North − South (km)

Hei

ght (

km)

(a)

−150−100

−500

50100

150

−100−50

050

100

0

0.5

1

1.5

West

− East

(km)


Hei

ght (

km)

(b)

−150−100

−500

50100

150

−100−50

050

100

0

0.5

1

1.5

West

− East

(km)


Hei

ght (

km)

(c)

−150−100

−500

50100

150

−100−50

050

100

0

0.5

1

1.5

West

− East

(km)


Hei

ght (

km)

(d)

Figure 5. Examples of the idealized terrain used in Paper I: (a) control run (Ctrl), also used in Paper II ; (b)z1_Cc24; (c) z4_α24; and (d) z1_cape500. Maximum height of the idealized terrain is 1.2 km.

STEFAN SÖDERBERG

14

also in Tjernström (1999) and was one of the questions Paper I was set up to resolve. In fact,a gradual acceleration of the flow along the upstream coastline was present in all i dealizedsimulations but the ones with capes. Burk et al. (1999) also found an increase in MABLwinds along the upstream coastline; however, this was in a transcritical simulation withsubcritical flow upstream of the bend. For the moment, we will l eave this issue and return toit in the next section. Instead we will take a look at the simulated vertical structure of thealong-coast MABL flow in Ctrl.

Vertical cross-sections of potential temperature and scalar wind speed taken from west toeast are shown in Figure 7. Upstream of the coastline bend, an oval-shaped wind-speed jet isfound near the inversion base, aligned with the maximum slope of the inversion close to

0

50

100

150

200

250

300

350

400

450

500

−150 −100 −50 0 50 100 150

−100

−50

0

50

10050

100

200

300

350

350

400

400

450

West − East (km)

Sou

th −

Nor

th (

km)

(a)

10

15

20

25

30

−150 −100 −50 0 50 100 150

−100

−50

0

50

100

10

11

13

1315

16

17

18

18

19

22

1920

20

21

West − East (km)

Sou

th −

Nor

th (

km)

(b)

0.5

1.0

1.5

2.0

2.5

−150 −100 −50 0 50 100 150

−100

−50

0

50

100

0.9 1

1

1.1

1.1

1.3 1.3

1.3

1.5

1.51.5

2

22

West − East (km)

Sou

th −

Nor

th (

km)

(c)

Figure 6. Contour plots from the control run of: (a) MABL depth (m); (b) maximum MABL wind speed(m s -1); and (c) Froude number.


15

coastline (Figure 7a). These model results are in most aspects representative of the balancedstate with a sloping inversion towards the coast as described by the conceptual model ofBeardsley et al. (1987, see Figure 3). Downstream of the bend, the slope of the inversionsteepens considerably and in the near-shore region the MABL collapses entirely (Figure 7b).High momentum air is found at low altitudes within the wide wind-speed jet, which also tiltsconsiderable towards the coastline as a result of the steeply sloping inversion.

The change of orientation of the real terrain along northern California is however not asabrupt as in Ctrl. Tjernström (1999) suggested that the gradual curvature of the main coastalmountains north of Cape Mendocino may be sufficient to excite an expansion fan. To testthis hypothesis, numerical simulations with curved coastlines were performed. Moreover,the terrain elevation also varies along the coast with the highest terrain north of CapeMendocino; therefore were the effects of terrain height variations on the MABLcharacteristics investigated. In Figure 8 maximum MABL wind speed from two of theseexperiments are shown, z1_Cc24 with a curved coastline (Figure 8a) and z4_α24 with adecreasing terrain height along the coast (Figure 8b). The simulations with curved coastlinesclearly il lustrated that the change in coastline orientation does not have to be abrupt to excite

−150 −100 −50 0 50 100 1500

0.5

1.0

1.5

2.0

2.5

2

44

4

6

6

6

8

8

10

19

12

14

14

16

1618 285

289

295

297299

301303305

307

309

311

West − East (km)

Hei

ght (

km)

(a)

−150 −100 −50 0 50 100 1500

0.5

1.0

1.5

2.0

2.5

21

2

2

2

4

4

4

6

6

8

8

8

10

12

1214

1618

20285

287289291 293 295

297 299

301303

305

307

307

309

311

West − East (km)

Hei

ght (

km)

(b)

Figure 7. East-West vertical cross sections of potential temperature (K) (dashed) and scalar wind speed(m s -1) (solid) from the control run: (a) upstream at y ~ 75 km; and (b) downstream at y ~ -50 km.

10

15

20

25

30

−150 −100 −50 0 50 100 150

−100

−50

0

50

100

1011

12

13

13

1415

17

19

20

20

20

21

21

2223

24

West − East (km)

Sou

th −

Nor

th (

km)

(a)

10

15

20

25

30

−150 −100 −50 0 50 100 150

−100

−50

0

50

100

10

10

10

11

11

12

12

12

13

13

1415

16

19

20

20

21

22

22

23

23

24

West − East (km)

Sou

th −

Nor

th (

km)

(b)

Figure 8. Contour plots of maximum MABL wind speed (m s -1) from: (a) z1_Cc24; (b) z4_α24.

STEFAN SÖDERBERG

16

an expansion fan, a curved coastline is sufficient. Terrain height variation along the coasthad a significant impact on the MABL flow. An additional along-coast acceleration of theflow took place and the marine air was able to stretch farther in over land due to the reducedblocking. The higher magnitudes of the wind speed can be explained by an intensifiedsecondary coastal circulation due to the lowering of the height of the coastal barrier,increasing the slope of the inversion towards the coastline further.

Previous studies have indicated that the local terrain at Cape Mendocino has a distinct effecton local flow characteristics. In our experiments with simplified capes, this was clearlydemonstrated. The terrain of the cape protruding into the flow caused a significant blockingof the upstream flow, even when the height of the cape was only half of the upstreamMABL depth. As an example, model results from z1_cape500 are shown in Figure 9.Upstream of the cape, the MABL depth is less than the height of the cape, which is 500 m(Figure 9a). As the flow passes the cape, it accelerates rapidly and forms a wind-speedmaximum similar in shape to that in Ctrl, but farther away from the main coastal mountainrange (Figure 9b). At the tip of the cape, the flow also becomes supercritical (Figure 9c);thus the flow is transcritical, a clear distinction from the control run. Furthermore, along thedownstream coastline, the near-shore wind speeds are also weaker than in Ctrl. Note inparticular the relatively low wind speeds found in the lee of the cape where the MABLcollapses entirely.

The effect of the cape on the MABL properties is further appreciated in Figure 10a, showingvertical cross sections of potential temperature and scalar wind speed taken from west toeast downstream of the cape. A substantial warming of the air below 500 m is found in thenear-shore region and the collapse of the MABL is apparent. Note also the skewed structureof the jet, tilti ng towards the coast, and the wedge of low-momentum air brought down fromaloft to low altitudes in the lee of the cape; this is another clear distinction from the resultsfound in Ctrl (cf. Figure 7b). In fact, observed flow features around Cape Mendocino andfindings in real-case studies with different numerical models are in many respectsreproduced in this idealized simulation (e.g., Rogers et al. 1998; Ström et al. 2001; Burk andThompson 1996; Tjernström and Grisogono 2000). It is therefore not too far-fetched toconclude that the terrain forcing induced on the MABL flow by the simplified terrain usedin z1_cape500 is representative of the real terrain forcing along the northern Californiacoast. In Paper I it was also found that the terrain at the cape triggers a lee-wave, assuggested from observations (Ström et al. 2001) and earlier model studies (Burk andThompson 1996; Tjernström and Grisogono 2000; Tjernström 1999). Moreover, consistentwith the extended flow regime diagram of Ólafsson and Bougeault (1996), gravity wavebreaking was found on the lee-side of the cape. A north-south cross section through the capein z1_cape500 is shown in Figure 10b. Note in particular the isotherms sloping steeplydownward in the along-flow direction and then rising quickly on the lee-side of the cape,where the low-level flow accelerates to more than 16 ms -1. Above the wind-speedmaximum, a local maximum in TKE is also found (not shown). In fact, a lee-wave wastriggered in all three experiments with capes. Thus, it is likely that terrain features such asthe local terrain at Cape Mendocino, to a large extent determine MABL characteristics inhigh-velocity along-coast flows.


17

The simulations performed in Paper I with simpli fied terrain allowed us to test hypothesisrelated to coastline geometry in a simple manner. We found that the model results in manyways conformed to the predictions of supercritical flow response, although differencesbetween shallow-water and three-dimensional models were il lustrated. When a simplifiedcape protruding into the flow was introduced, the flow characteristics agreed well withobservations along the northern California coast, suggesting that capes and points withprominent terrain largely determine the MABL characteristics. However, an unexpectedfeature appeared in all simulations but the ones with simplified capes. Along the upstreamcoastline a gradual acceleration of the flow occurred which appears to violate the hydraulictheory if the flow is truly supercritical. Paper II was set up with the aim to resolve thispuzzle.

0

50

100

150

200

250

300

350

400

450

500

550

600

−150 −100 −50 0 50 100 150

−100

−50

0

50

100 500

1050100

200

300

400

450

450

West − East (km)

Sou

th −

Nor

th (

km)

(a)

5

10

15

20

25

−150 −100 −50 0 50 100 150

−100

−50

0

50

100

10

10

10

10

12

1216

14

1610

17 18

1819

1920

West − East (km)

Sou

th −

Nor

th (

km)

(b)

0.5

1.0

1.5

2.0

2.5

−150 −100 −50 0 50 100 150

−100

−50

0

50

100

0.70.8

0.9

0.9

0.9

1

1 1

1

1

1

1.1

1.1

1.1

1.1

1.3

1.3

1.3

0.8

1.31.5

1.5

1.5

1.5

22

2

2

2

West − East (km)

Sou

th −

Nor

th (

km)

(c)

Figure 9. As Figure 6 except for z1_cape500.

STEFAN SÖDERBERG

18

3.1.3 Transient behavior of supercritical MABL flows

In Paper I it was observed that the only experiments that did not feature a gradualacceleration of the flow along the upstream coastline were the experiments with simplifiedcapes inserted perpendicular to the main coastal mountain barrier. Another significantfeature in the simulations with capes was the transition from subcritical to supercritical flow,when the flow passes the cape. Thus, the results in Paper I suggests that the absence of agradual upstream acceleration in the observations from Cape Mendocino may be due to thepresence of blocking terrain at the cape and not the supercriticali ty of the flow. Onehypothesis offered in Paper I as the cause of the upstream acceleration of the flow was basedon the fact that the initial profile used in all simulations is actually subcritical. Thesupercriticali ty of the flow then develops during the dynamic initialization of the model,which would allow the gradual acceleration of the flow to be established along the upstreamcoastline during the subcritical phase of the simulation. The transient behavior of the flowwas therefore studied in Paper II .

If we take a step back and consider the diurnal variation of the MABL in the near-shoreregion described by Beardsley et al. (1987), a plausible explanation for the deviation fromthe original hydraulic theory emerges (see Figure 11). During night when the temperaturecontrast between land and the MABL is small or negligible, the slope of the inversiontowards the coast is also gentle. Close to the coast, the MABL winds are therefore relativelyweak. In the morning when the sun heats the land surface, the air destabili zes, allowing for apenetration of the MABL air over land. At the same time, the slope of the inversion towardsthe coast increases. Above the eroded inversion over land, a weak return flow helpsdepressing the near-shore inversion further. As a result, a strong low-level jet is often foundadjacent to the coastal mountain range.

−150 −100 −50 0 50 100 1500

0.5

1.0

1.5

2.0

2.5

2

22

4

46

6

8

8

8

20

10

10

12

12

16

18 285

287289291

293

295

297299299

301301

303303

305

307

309

311

West − East (km)

Hei

ght (

km)

(a)

0 10 20 30 40 50 0

0.25

0.50

0.75

1.00

1.25

1.50

11

2

4

4

16

6

14

8

10

10

10

12

287

289

291293

295297299

301

303

South − North (km)

Hei

ght (

km)

(b)

Figure 10. (a) East-West vertical cross section at y ~ -50 km of potential temperature (K) (dashed lines) andscalar wind speed (m s-1) (solid lines) from z1_cape500. (b) North - South cross section at x ~ -5 km ofscalar wind speed (m s-1) (solid lines) and, potential temperature (K).


19

This diurnal variation of the MABL is reproduced in Paper II; descriptions of theexperiments performed are found in Table 1 of Paper II . Early in the morning a relativelyweak jet is found far offshore below a gently sloping inversion (Figure 12a). The well-mixed MABL close to the coast is about 400 m deep. In the afternoon the depth of theMABL have decreased notably. The jet is now attached to the main coastal mountains, andis considerable stronger than during night, as a consequence of the increased slope of theinversion close to the coast (Figure 12b). Two factors that have a direct effect on the flowcriticali ty are here easily identified: a low flow velocity and a deep MABL results in asubcritical flow during the night, while a high flow velocity and a shallow MABL producesa supercritical flow during the day. The resulting diurnal variation of the flow criticali ty isill ustrated in Figure 13. Thus, during nighttime and early in the morning when the flow issubcritical, the gradual acceleration of the flow can take place along the upstream coastline,without violating the hydraulic theory. This feature will then disappear only very slowly,once the flow becomes supercritical. Together with results the from Paper I this suggeststhat daytime supercritical conditions may not prevail suff iciently long for a true quasi-steady-state supercritical flow to be established in the absence of blocking terrain protrudinginto the flow. Furthermore, Paper II shows that the gradual acceleration of the flow alreadyupstream of the change in coastline orientation is not violating the hydraulic theory and thatthe flow criticali ty in MABLs similar to what is found off the U.S. west coast does not onlyvary spatiall y, but also temporally.

Figure 11. Conceptual model of lower atmosphere over the nearshore zone during night (top) and day(bottom). (From “Local atmospheric forcing during the coastal ocean dynamics experiment. 1. A descriptionof the marine boundary layer and atmospheric conditions over a northern Cali fornia upwelling region,” R. C.Beardsley, C. E. Dorman, C. A. Friehe, L. K. Rosenfeld, and C. D. Winant, J. Geophys. Res., 92: 1482, 1987.)

STEFAN SÖDERBERG

20

3.2 The katabatic jet

Katabatic flows, also known as drainage or gravity flows, are formed when the air adjacentto a sloping surface cools more than the air at the same elevation, but away from the surface.This triggers a low-level downslope flow since the negative buoyancy will act alsohorizontally, the so-called katabatic forcing term. In general downslope flows can form onany sloping surface. However, the katabatic forcing is usually smaller than the other termsin the momentum budget, such as the synoptic pressure gradient. Thus, katabatic flows aretypically only observed during clear sky conditions, when nighttime radiative cooling of thesurface peaks. Over icecaps on the other hand, the katabatic forcing term in most casesappears strong enough to overcome the background pressure gradient term. Persistentkatabatic flows over glaciers have been reported in numerous studies, some of which arereferred to in the present thesis (e.g., Gruell et al. 1994; Oerlemans et al. 1999).

The simplest theory for katabatic flows is the classic Prandtl model (Prandtl 1942), in whichthe advected background temperature lapse rate and the buoyant acceleration are balancedby the divergence of the turbulent fluxes of heat and momentum, respectively. In acoordinate system with its axes aligned with the slope, the equations read:

( ) ( )0=

∂∂+γ

z

''wsinu

θα , (8)

( ) ( )0

0

=∂

∂−αz

'u'wsing

θθ

. (9)

where γ is the background potential temperature lapse rate, u is now the downslope windspeed and w the velocity perpendicular to the slope, while α is the slope of the surface. Hereθ is the potential temperature perturbation, θ0 a reference temperature (in the present thesisthe potential temperature of the ambient air). Overbars indicate an averaging operation andprimed terms are deviations from the average. Using K-theory and assuming constant values

−150 −100 −50 0 50 100 1500

0.5

1.0

1.5

2.0

2.5

17

4

4

4

6

6

8

8

8

10

12

14

14

16

285

291293

295297

299301

303

305

305307

307

309

West − East (km)

Hei

ght (

km)

(a)

−150 −100 −50 0 50 100 1500

0.5

1.0

1.5

2.0

2.5

2

19

4

4

4

6

6

8

8

10

12

12

14

14

16

1618

287

297

299301

303

305305

307

309

West − East (km)

Hei

ght (

km)

(b)

Figure 12. Vertical cross-sections of potential temperature (K) (dashed lines) and scalar wind speed (m s-1)(solid lines) from exp_restart taken upstream of the bend at y ~ 75 km: (a) 0600 LST; and (b) 1500 LST.


21

of the eddy diffusivities for momentum and heat, Km and Kh, the equations are analyticallysolvable with the solution:

( ) ( )z sineCzu z δµ−= δ− , (10)

( ) ( )z cosCez z δθ δ−= , (11)

in which C is the surface temperature deficit, ( ) 00 <= Cθ , and

50

0Pr

.g

γ

=µθ

, (12)

( ) 50

Pr2

.

hK

sinN

α=δ , (13)

where Pr is the eddy Prandtl number defined as the ratio between Km and Kh, and N is thebuoyancy frequency

0θg

Nγ= . (14)

One of the main deficiencies of the Prandtl model is that the near-surface gradients of thecalculated quantities are too weak. This is because the eddy diffusivities are assumedconstant and do not decrease when the surface is approached. Another deficiency is that theheight of the jet in the Prandtl model does not increase with the strength of the jetmaximum, which is found in observations (e.g., Oerlemans and Grisogono 2002).

To overcome the latter problem, Oerlemans and Grisogono (2002) defined scales that whenput into the Prandtl model, characterize a katabatic state. In their analytical model, theyended up with three equations predicting steady state jet strength (um), jet height (zm), andsurface sensible heat flux (Fh), from background parameters:

12 13 14 15 16 17 18 1910

11

12

13

14

15

16

Mean MBL wind speed (ms−1)

Pha

se s

peed

(m

s−1 )

18(start)

24

06

12

18 (end)

Figure 13. Diurnal cycle of phase speed and mean MBL wind speed for exp_restart. The numbers along thesolid line show local standard time while the dashed line indicates where Fr = 1.

STEFAN SÖDERBERG

22

50

01

2

Pr

.

mg

Ck

ku

γ

−=θ

, (15)

( )αγ−=

sin

C

k

kkzm

3

2 , (16)

50

0

222 Pr

.

hg

CkkF

γ

−=θ

. (17)

However, the empirical constants k, k1, k2, and k3, are yet to be determined, and as pointedout by Oerlemans and Grisogono (2002), the currently available observational data does notallow for a determination of these constants.

In Paper IV the aim was to compare the predictions of the analytical model described abovewith katabatic flow characteristics as simulated and modeled by a “state of the art”mesoscale numerical model. Since the constants in (15)-(17) are unknown, the test had to bedone in three steps.

• First a realistic behavior of COAMPS was verified by comparing results from a real-datacase study to observations; the horizontal model domains are shown in Figure 2.

• Then a series of idealized numerical simulations were set up with conditions similar tothose of the analytical scaling. This allowed us to find estimates of the undeterminedconstants.

• Finally, the analytical model was applied to the real-data simulation of the katabatic flowover Breidamerkurjökull , and its predictions of um, zm, and Fh from simulatedbackground parameters, were compared to the corresponding quantities, as simulatedand modeled by COAMPS.

The location of some of the observational stations put on Breidamerkurjökull during the1996 Glacio-Meteorological field experiment (Oerlemans et al. 1999), are shown in Figure14. Also shown is the simulated near-surface flow over Breidamerkurjökull . From the top ofthe glacier and down towards the ocean, the flow accelerates and turns into the glacier fallline. To further il lustrate the spatial variation of the simulated flow overBreidamerkurjökull , Figure 15 shows vertical cross sections of temperature and themeridional wind component, taken along B-C in Figure 14. Even though this cross-section isnot along a trajectory, it provides a good view of what an airparcel may experience on itsway from the top of Breidamerkurjökull down towards the ocean. In the upper part of theglacier, the temperature deficit is small . As one moves down the glacier, the atmospherictemperature increase adiabatically, while the surface temperature is constant at meltingpoint; the temperature deficit experienced by an airparcel as it progresses down the glacier,therefore will increase. In response to the increased katabatic forcing, the flow acceleratesand forms a wide low-level jet, covering a large part of Breidamerkurjökull . Anotherconsequence of the adiabatic heating is that the buoyancy force will continuously increasealong the trajectory, and in this sense, the katabatic flow drives itself.


23

A principal agreement between observed and simulated flow-characteristics overBreidamerkurjökull was found in Paper IV, ensuring a realistic behavior of COAMPS.Scaling arguments also provided support for classifying the simulated low-level flow as ashooting flow, within the dynamical regimes for downslope gravity flows organized byMahrt (1982). This type of flow is defined as a three-term momentum balance between thebuoyancy term, downslope advection and turbulent transport. Our scale analysis alsorevealed that cross-slope advection can be of importance in the downslope momentumequation. Encouraged by these results, we continued the work in finding estimates of theunknown empirical constants in the analytical theory. Model results from the idealizedexperiments, emulating the conditions of the analytical scaling, were used to calculate theconstants. The maximum simulated downslope wind-speeds plotted versus um from theidealized simulations and from the real-data simulation are shown in Figures 16a and 16b,respectively. The simulated wind speed and predicted wind speed from the analytical modelline up quite nicely around the one-to-one line, providing the value of the constant. In thereal-data simulation, a reasonable agreement between simulated and estimated values of thewind speed is found. However, some discrepancies are apparent, primarily in the lower partof the glacier and where the simulated jet height is above 10 m; here the simulated windspeed have a magnitude much higher than that predicted by the analytical model. Similarobservations were also made for the jet height and the downward directed surface sensibleheat flux.

−16.6 −16.55 −16.5 −16.45 −16.4 −16.35 −16.3 −16.25 −16.2 −16.15 −16.163.8

63.85

63.9

63.95

64

64.05

64.1

64.15

64.2

64.25

64.3

64.35C

B

Longitude

Latit

ude

1

1

1

1

1

2

2

2

2

34

I6

A5A4U3

U2

Figure 14. Scalar wind speed (dashed) and wind vectors at 11 m height 7 July 12 UTC in the immediatesurroundings of Breidamerkurjökull . Terrain elevation is contoured every 100 m; coastline is bold.Observational stations and their positions are indicated by dots (Oerlemans et al., 1999). Stars show gridpoints used in the estimates of surface sensible heat flux and katabatic jet height and strength in section 3.2.The cross-sections shown in Figure 15 are taken along B-C.

STEFAN SÖDERBERG

24

From the observations described above and the fact that the wind-speed maximum in theidealized experiments was found at 10 m height or below, one possible reason for theanalytical underestimation of the wind speed in the real-data experiment, can be theproximity of the jet to the surface. In Paper IV it was hypothesized that local effects, such assurface inhomogeneity and slope geometry, absent in the idealized experiments but certainlypresent in the real-data simulation, lifts the jet to a higher height than it would have beenfound at, in the pure katabatic flow conditions assumed in the analytical model. As a result,the magnitude of the wind speed will also increase since the effect of friction decreases withheight. In the real-data simulation, the analytical model therefore will underestimate the jetheight, the wind speed and also the surface sensible heat flux, since the latter depends on thekatabatic velocity scale.

63.8 63.85 63.9 63.95 64 64.05 64.1 64.15 64.2 64.25 64.3 64.35 0

0.5

1.0

1.5

Ele

vatio

n (k

m)

63.8 63.85 63.9 63.95 64 64.05 64.1 64.15 64.2 64.25 64.3 64.350

20

40

60

80

100

120

140

160

180

200

Latitude

Hei

ght a

gl (

m)

−4−3

−2

−2 −2

−1

−1−1

−1

0

0

0

0

1

1

1

1

2

2

272

274276278

280

282

282

Figure 15. Cross-section along B-C of Figure 14 of the meridional wind component (solid) and temperature(gray dashed) at 12 UTC 7 July. Vertical axis is in m above ground level. Terrain elevation in km above sealevel along the cross-section is also shown. Negative values of the meridional wind component are heredirected close to the glacier fall li ne.


25

4. Boundary-layer characteristics in the presence of low-level jets

In the presence of a low-level jet, the boundary-layer structure is often dominated, or at leastsignificantly influenced, by the vertical wind-shear. This is because shear-generatedturbulence acts to mix boundary-layer properties such as temperature and humidityvertically. If the boundary layer is stable enough, the mixing can however be suppressed.Moreover, the boundary layer structure can be significantly altered if the low-level jetencounters complex terrain.

As an example, Figure 17 displays two characteristic MABL profiles of observed andsimulated potential temperature and wind speed in the vicinity of Cape Mendocino. Oneprofile is taken upstream of the cape and the other within the expansion fan downstream ofthe cape (see Paper III for details). In addition to the effects of the wind-speed jet, the SSTvariation along the coast, also influences the boundary-layer structure. This can be seen inthe observed potential temperature profile upstream of the cape, indicating a stable internalboundary layer in the lowest 300 m of the MABL. The model does not capture the internalboundary layer in detail although the wind-speed profile is fairly well reproduced.Downstream of the cape the vertical structure of the MABL is more intricate. The MABLflow has accelerated and the MABL depth has decreased significantly in response to thealtered terrain forcing and the lee-wave induced by the cape; still the model does a fair jobin reproducing the observed features.

Another example of a boundary layer dominated by a low-level jet, is found overBreidamerkurjökull and studied in Paper IV. Figure 18 shows observed and simulatedvertical profiles of temperature and wind speed from the upper and lower part ofBreidamerkurjökull . One of the most striking differences between the MABL and thekatabatic layer is that the jet is found below the inversion in the former and within theinversion-layer in the latter. Due to the proximity of the jet to the surface, the near-surface

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

8

Max

imum

dow

nslo

pe w

ind

(m s

−1 )

um

(m s−1)

α = 20

α = 40

α = 60

α = 80

(a)

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

um (m s−1

)

Max

imum

dow

nslo

pe w

ind

(m s

−1 )

uppermid lower

(b)

Figure 16. Maximum simulated wind speed plotted versus the analytical estimate, um from (a): Idealsimulations, the markers represent different slope angles according to legend; solid line is a one-to-one line.(b) Real-case simulation, the markers indicate in which third of Breidamerkurjökull along the fall li ne thevalues are taken. Black markers indicate grid points with a wind maximum below 10 m height; grey markersindicate a wind maximum between 10 and 30 m height; 825 data points are plotted.

STEFAN SÖDERBERG

26

vertical wind-shear is substantial. Moreover, the shear is more or less confined to thekatabatic layer. In contrast to this, strong vertical wind-shear is also found at higher altitudesaround the inversion in the MABL. When comparing the simulated flow characteristics toobservations, it is apparent that the simulated inversion layer is too deep compared to theobservations; the simulated jet height and magnitude are also too high. In Paper IV it isspeculated that this might be due to a too vigorous vertical mixing close to the surface. Onediff iculty in directly comparing simulations to observations in complex terrain was alsohighlighted here. Due to the finite horizontal resolution in the model, the difference interrain elevation between station A4 and closest the grid point was in fact ≈ 225 m. Theobserved temperature profile agrees better with the simulated temperature profile from amodel grid point where the terrain elevation agrees better with the actual height of stationA4 above sea level.

278 280 282 284 286 288 290 292 294 296 298 300 302 3040

100

200

300

400

500

600

700

800

900

1000

θ (K)

Alti

tude

(m

)

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 280

100

200

300

400

500

600

700

800

900

1000

Wind speed (ms−1)

Alti

tude

(m

)

(b)

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

70

80

90

100

Hei

ght (

m)

m s−1; oC

(a)

0 1 2 3 4 5 6 7 8 9 100

10

20

30

40

50

60

70

80

90

100

Hei

ght (

m)

m s−1; oC

(b)

Figure 17. (a) Profiles of potential temperature upstream of Cape Mendocino (dark line) and within theexpansion fan (gray line). The dashed lines show profiles from the model for all the grid points spanned bythe aircraft slant-profile. The top of the internal boundary layer is indicated by an arrow. (b) The mean windspeed for the same locations as in (a). See Paper III for details.

Figure 18. Observed scalar wind speed (diamonds) and temperature (circles) from profile mast. Simulatedscalar wind speed (solid) and temperature (dashed) from: (a) station A5; and (b) station A4. Also shown in(b) is a temperature profile from the model grid point due south of the one closest to station A4 (dash-dotted). The difference in terrain elevation between the two gridpoints is ~310 m. Scalar wind speed (solidgray) and temperature (dashed gray) from the tethered balloon sent up from station U3 are also shown in (b).


27

One may ask why the linear hydraulic theory presented in section 3.1.2 has provensuccessful in describing the flow off the U.S. west coast, in spite of the apparent differencesdiscussed in Papers I-II . Among the assumptions in the theory is a single flow velocitywithin the layer, while the actual MABL features a wind-speed jet. For the singe-layerreduced gravity theory to be applicable, the MABL must also be separated from the freeatmosphere above, since the theory assumes that all gravity-wave energy resides within aninfinitesimally thin inversion. Burk et al. (1999) proposed that wave trapping could be theprocess responsible for the separation of the MABL from the free atmosphere above. Theybased their conclusion on calculations of the Scorer parameter L2, which within linear theoryis defined as (e.g., Nappo 2002):

2

2

2

22 1

z

U

UU

NL

∂∂−= . (18)

Burk et al. (1999) found small and often negative values of L2 above the coastal jet,implying that verticall y propagating buoyancy waves are not possible; instead the wavesdecay exponentially with height. Small or negative values of L2 are due to that the curvatureterm in (18) becomes large compared to the buoyancy term, a characteristic of the jet itself.This conclusion is not only interesting as a physical explanation for the observedsupercritical flow-response around coastal bends, but also in a more philosophical way. Thatis, the presence of a wind-speed jet below the inversion, instead of a uniform layer-velocityas assumed in the hydraulic theory, may in fact be the very reason for the success of thehydraulic theory, in describing observed characteristics of the MABL flow along the U.S.west coast.

Since wave trapping is common when wind-speed jets are present (Nappo 2002), this pointsto a generali ty for boundary layers dominated by low-level jets, namely that they areeffectively shielded from the free atmosphere above. From observations overBreidamerkurjökull , Parmhed et al. (2004) hypothesized that wave trapping could beimportant for the persistence of katabatic flows. In Paper IV we calculated L2 from modelresults and a contour plot typical for the lower part of Breidamerkurjökull is presented inFigure 19. The deep layer with negative values of L2 is a clear indication of persistent wavetrapping above the katabatic jet and a decoupling of the near-surface flow from the ambientflow aloft. Although several observational studies have pointed out that katabatic flows arepersistent over glaciers, even at locations like Vatnajökull in the middle of the north Atlanticstormtrack (e.g., Smeets et al. 1998; Oerlemans et al. 1999), none have given a physicalexplanation for this. Our results suggest that wave trapping effectively separate the jet fromthe flow aloft. The trapping is a consequence of the vertical structure of the jet itself, andtherefore will katabatic flows over glaciers be persistent, as soon as they are established.

STEFAN SÖDERBERG

28

5. Turbulence structure in stable boundary layers

Whenever the surface is cooler than the air, the boundary layer usually becomes stablystratified. One physical process leading to the formation of stably stratified boundary layersis radiative cooling, which often is the case at night over land. Another process is advectionof warmer air over a cooler surface. This can lead to the formation of an internal stableboundary layer like in Paper II I. Although stable boundary layers are common, they are stillpoorly understood and not well described in numerical weather and climate models (e.g.,Poulos et al. 2002). One of the reasons for that may be that the stable boundary layer hasbeen less widely studied than its neutral or convective counterparts. Other reasons can bethat turbulence in stable boundary layers is weak and often co-exists with gravity waves(e.g., Nappo and Johansson 1999). Measurements at a single location may also not berepresentative of the area as a whole due to spatial heterogeneity. Moreover, turbulence instably stratified boundary layers can also be sporadic and patchy. This is because shear-generated turbulence, or mechanically generated turbulence, is suppressed by negativebuoyancy. Depending on the magnitude of these two competitors, stably stratified boundarylayers can range from well mixed to essentially nonturbulent. This sets a limit for how wellan ensemble-average numerical model can simulate atmospheric processes in stableboundary layers since this type of closure, by its very nature, cannot describe sporadicturbulence. Furthermore, in ensemble-average numerical models, the turbulence is modeledrather than simulated.

0 3 6 9 12 15 18 21 240

20

40

60

80

100

120

140

160

180

200

Time (UTC)

Hei

ght (

m)

−0.2

−0.1

−0.1

−0.1

−0.1

0.5 0.50.50.5 0.5

0.50.51 11 1 11 111.5 1.51.5 1.50

0

0

0

0

00

0

0 00 0

0

Figure 19. Contour plot of the Scorer parameter, L2 .10-2, from the model grid point closest to station A4.Bold lines are 0-isolines.


29

The stabili ty range is often the discussed in terms of the gradient Richardson number Rig(e.g., Stull 1988):

∂∂+

∂∂

∂∂=

22

z

v

z

u

z

gRi v

vg

θθ

, (19)

where u and v are now the along-wind and cross-wind components, and θv the virtualpotential temperature. The z-axis is now again aligned with the gravity vector, as is thevertical velocity, w. Note that in general 0≠∂∂ zv even if 0≡v , except in the surface layerwhere the wind direction is usually assumed constant. It is often assumed that when Rigexceeds a critical value, turbulence will cease to exist.

Near a local wind-speed maximum, the shear-term becomes small and the stabili ty thereforeincreases. This is il lustrated in Figure 20 showing the relation between Rig and the jet heightfrom the simulated katabatic flow over Breidamerkurjökull . The values of Rig are here takendirectly from the turbulence closure scheme utili zed in the numerical model. It is clear thatthe highest stabiliti es are found close to the wind-speed maximum. Above the jet there isalso a tendency for the scatter among the Rig profiles to increase. These model results agreewell with observations of katabatic flow over the Pasterze glacier in Austria (Smeets et al.2000), although the Rig profiles appear smoother here. A reason for this may beuncertainties in the calculations of the wind-speed gradient near the wind-speed maximum,both in observations and in the numerical model. It may also be an artifact, since Smeets etal. (2000) plotted individual data points from fixed instruments, above and below the wind-speed maximum, while we instead plot continuos profiles, connecting associated data pointsacross the wind-speed maximum.

0.05 0.2 0.5 1 2 5 20 50 2000

0.5

1

1.5

2

2.5

3

Rig

z / z

jet

Figure 20. Dimensionless height z / zjet plotted versus Rig from 00 to 24 UTC 7 July 1996. Profiles are takenfrom the grid points marked with stars in Figure 14.

STEFAN SÖDERBERG

30

To further il lustrate the vertical turbulence structure of stable boundary layers in whichwind-speed jets are present, profiles of the modeled momentum flux overBreidamerkurjökull and from within the expansion fan in the lee of Cape Mendocino areshown in Figure 21. The height of the jet, zjet, has been used to normalize z in Figure 21a,while in 21b we instead have used the MABL depth zi, defined as the height at which themomentum flux falls to 1% of its surface value. Note that although the parameters used toscale z are not identical, the momentum flux profiles scale in a similar way. This highlightsthe difficulty of defining one unique length scale for the stably stratified boundary layer, aswill be discussed below. However, in the present case the two length scales converge since

'w'u approaches zero close to the wind-speed maximum.

A striking feature in the profiles of normalized momentum flux, are the high magnitudes ofupward directed flux above the wind-speed jets; this is distinct from stable boundary layersin general. Above the katabatic jet, upward momentum flux reaches 40% of its surfacevalue; the high values are due to a reduction in static stabili ty in the katabatic layer, whilethe wind shear remains relatively strong. Above the MABL wind-speed maximum, evenhigher values of the normalized momentum flux are found, reaching magnitudes up to 80%of the surface values. Interesting to note is that the high values are all from the coastal sideof the jet. In Paper III it was speculated that this is due to advection of warm inland airoffshore, as a result of the secondary circulation around the jet observed in Paper I. Thisreduces the static stabil ity to a point where the Richardson number becomes subcritical andturbulence can be sustained above the jet. Profiles from the offshore side of the coastal jethave in fact relatively low magnitudes of momentum flux above the jet, not exceeding 5%of their surface values; this is also less than for most of the profiles above the katabatic jet.

In Figure 21 we have also plotted the normalized profile suggested by Lenshow et al. (1988)for stable stratification (thick solid line). Yet another difference between the two boundarylayers is here apparent. In the katabatic boundary layer, the profiles are more concave thanthe analytical li ne. This is due to an increased momentum flux at the surface as the low-level

−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.80

0.5

1

1.5

2

2.5

3

<uw> / u*2

z / z

jet

(a)−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.80

0.5

1

1.5

2

2.5

3

<uw>/u*2

z/z i

(b)

Figure 21. Simulated momentum flux normalized by the square of the surface friction velocity plottedagainst normalized altitude from (a): Breidamerkurjökull , 00 to 24 UTC 7 July 1996, from the grid pointsmarked with stars in Figure 14. (b) The expansion fan in the lee of Cape Mendocino. The solid line in (a)and (b) is the profile suggested by Lenshow et al. (1988) for stable stratification.


31

flow continuously accelerates on its way down the glacier. The proximity of the jet to thesurface also contributes to the concave profile because the magnitude of the momentum fluxmust decrease rapidly, as the wind-speed maximum is approached from below. In theMABL, the normalized momentum flux profiles are either more concave or convex than theprofile suggested by Lenshow et al. (1988). This is a result of a combination of changes inMABL depth, wind speed, wind shear, and momentum flux at the surface, in the along-coastflow. When the flow accelerates in the upwind portion of the expansion fan, the momentumflux at the surface also increases, giving rise to a concave profile; this is similar to what isfound over Breidamerkurjökull . Where the flow speed is the highest, the combined effect ofa rapid decrease in MABL depth and an enhanced mixing due to an increased vertical wind-shear acts toward a more linear profile. As the flow speed decreases in the downwindportion of the expansion fan, so does the momentum flux at the surface, which produces aconvex profile of the normalized momentum flux.

It was pointed out above, that one of the difficulties in studies of stable boundary layers liesin defining a representative length scale of turbulence. Turbulent variables have traditionallybeen scaled in terms of the surface-layer fluxes as a function of z / h, where h typically is theboundary layer height. However, in stable conditions vertical motions are restricted andturbulent eddies can for that reason not extend over the whole boundary layer. The use of has a characteristic length scale is consequently not always the correct choice in stableboundary layers. Moreover, the height h itself is not uniquely defined in the stable boundarylayer. It is sometimes defined using the temperature profile, sometimes using the TKE, andsometimes at the wind-speed maximum. All these heights may be different in the stableboundary layer. To circumvent this problem, Niewstadt (1984) instead introduced the localscaling hypothesis, with scales defined in a manner analogous to the Monin-Obukhovscales. These scales, however, depend on local turbulence quantities at the actual height,rather than surface values; one can consider Niewstadt's theory as an extension of the ideasof Monin-Obukhov similarity theory above the surface layer. The local similarity scalesreads:

( ) 25022 .

L 'v'w'u'wu += , (20)

LL u''w θθ −= , (21)

( )vvLL ''wguL θκθ3−= , (22)

where κ is the von Kármán constant (taken as 0.40), uL local friction velocity, θL localtemperature scale, and LL the local Obukhov length.

As the stabili ty parameter z / LL becomes large, the theory of Niewstadt (1984) predicts thatlocally scaled quantities should approach a constant value. This is also what has been foundin several observational studies in different environments, although with a not insignificantscatter between studies (e.g., Sorbjan 1986, 1987; Horst and Doran 1988; King 1990;Brooks and Rogers 2000). However, in most studies the range of stabil ities has been limitedand general applicabili ty has not yet been demonstrated. Shao and Hacker (1990) included awider range of stabil ities in their study and found that instead of coming close to a constant

STEFAN SÖDERBERG

32

value as predicted by theory, the scaled variances actually increased in a well-orderedmanner at high stabil ities. Pahlow et al. (2001) and Al-Jiboori et al. (2002) havesubsequently reported similar results, although with different stabili ty dependencies.

In Paper III local scaling was applied to the standard deviation of the velocity componentstaken from observations off the California coast. Figure 22a shows the scaled standarddeviation of vertical velocity variance plotted against z / LL. A division of the individualestimates have been made into those from within the expansion fan (circles) and those fromoutside the fan (triangles). Although the scatter is significant in both sets, there is nosystematic difference between them. The heavy solid line shows the best-fit curve to ourobservations; for comparison curves found by other investigators are also plotted. Modeledvertical velocity variance scaled in the same way as the observations are shown in Figure22b, along with the best fit to the observations. An excellent agreement between theempirical function and the model results is evident from here; moreover, no systematicdifference in scaling behavior between regions with distinct flow dynamics can bediscerned. Similar results were also found for the observed and modeled horizontal velocityvariances (not shown).

These findings point to some significant results. The successful scaling of the velocityvariances in a highly perturbed environment, such as in the MABL studied in Paper III ,suggests that local scaling is a robust feature and can be expected to apply widely. Thesuccessful scaling of the modeled velocity variances also provides a strong validation for theturbulence closure scheme utili zed in the model. At the same time it indicates a generali ty inthe observational results since the model results depend on a turbulence closure derivedfrom completely independent experimental data. However, although the empirical functionsfound in Paper III have a similar form to those observed by several previous studies (Shaoand Hacker 1990; Pahlow et al. 2001; Al-Jiboori et al. 2002), some differences aresignificant, in particular at high stabiliti es. This poses the question as to what can be thecause of such substantial differences in the observed scaling functions. Moreover, thedeparture from the constant values predicted by Nieuwstadt's original theory has not yetbeen explained.

One of the assumptions in the local similarity theory is horizontal homogeneity, anassumption widely used in the search for suitable parameterizations of atmosphericturbulence processes, since it simplifies the problem substantially. In Paper II I this evidentlyis not a valid assumption. Another assumption is that the turbulence transport terms aresmall in stable conditions and therefore negligible. We hypothesize that the form of thescaling functions are controlled by non-local transport terms, such as advection, andturbulent and pressure transport terms, in the TKE budget, and that the curves represent thecontrolled breakdown of true local similarity. Since non-local processes may differsignificantly between different data sets, the scaling functions will differ between studies.Changes in non-local transport may also be responsible for some of the scatter in theobservations within one data set.


33

100

101

102

0

1

2

3

4

5

6

7

8

9

10

σ w/u

L

z/LL

(c)

10−3

10−2

10−1

100

101

102

103

0

1

2

3

4

5

6

7

8

9

10

σ w/u

L

z/LL

(b)

10−3

10−2

10−1

100

101

102

103

0

1

2

3

4

5

6

z/LL

σ w/u

L

out of fanin fan

(a)

Figure 22.. Scaled standard deviations of the vertical velocity component from the MABL off northernCali fornia, normalized by the local velocity scale and plotted against the stabil ity parameter z / LL (a):Observed turbulence quantities; the thick solid line is a best fit to our entire data set, the dashed line is theempirical function found by Pahlow et al. (2001), the dotted line the function found by Shao and Hacker(1990), and the thin solid line the function obtained by Al-Jiboori et al. (2002). (b): Modeled turbulencequantities; the heavy dashed line is the best-fit curve from the observations, see (a). (c) As (b) but for pointsabove the top of the modeled boundary layer. The heavy dashed line is the same as above while the dottedline is the constant value approached at near-neutral conditions. The circles are observational data obtainedin the turbulent region above the expansion fan.

STEFAN SÖDERBERG

34

The modeled vertical velocity variance is plotted also in Figure 22c, however this time, thedata points are taken from above the jet in regions with sustained turbulence (see Figure21b). Also shown are observations from the turbulent region above the expansion fan(circles). The scaled variances show a significant scatter and the well-defined functionalrelationship with stabili ty appears to break down. Nevertheless, the normalized variancevalues are limited on the high side by the empirical function and on the lower side by aconstant value near the neutral l imit of the scaled variance. If our hypothesis that the form ofthe scaling functions to a high degree are controlled by non-local transport terms is true,then the scatter in the figure could be explained by differences in non-local processes in thevolume sampled. The densest population of points lies close to the constant defined byneutral conditions, representing conditions where turbulent processes are truly local. Othergroups of points appear to line up along curves of similar shape, and may represent regionswith similar non-local transport. The break down of the scaling, and the limitations in thescatter, is also observed for the two horizontal velocity variances (not shown).

To test our hypothesis that non-local processes control the form of the scaling functions, weturn to a different environment. Local similarity scaling has previously been applied toobservations over Breidamerkurjökull (van der Avoird and Duynkerke 1999; Smeets et al.1999). In both these studies the scaled variances were close to the constant values suggestedby Nieuwstadt's (1984) original theory. However, the stabilit y ranges covered were limited,only up to z / LL = 1 in van der Avoird and Duynkerke (1999), and up to z / LL = 0.2 inSmeets et al. (1999). Horst and Doran (1988) also applied local scaling to katabatic flowwith success, yet again within a limited stabili ty range. Moreover, they only consideredturbulent quantities above the wind-speed maximum. In this thesis, turbulence quantitieshave been diagnosed from the COAMPS simulation of katabatic flow overBreidamerkurjökull; the scaled velocity variances σu, σv, and σw are shown in Figure 23along with the empirical functions found in Paper III . The scaled variances have also beenpartitioned into groups by normalized height according to the legends.

At first sight, the velocity components appear to follow a functional relationship similar tothe empirical functions found in Paper III (solid lines). Nevertheless, some substantialdifferences in scaling behavior between the two environments must be pointed out. Notefirst the absence of data points at the near-neutral side of the stabil ity range, or weakly stablecases as defined by Mahrt et al. (1998). The curvature of the data-point cluster for the along-wind component also appears less steep than the empirical function; at the highest stabiliti esthe points are on the lower side of the empirical function (Figure 23a). More apparent arethe differences for the cross-flow velocity variance (Figure 23b). Most of the data points liewell above the empirical scaling function and the curvature of the data-point cluster does notrise as quickly as the empirical function at high stabiliti es. In fact, the scaled cross-flowvelocity variances group closer to the empirical function for the along-flow velocityvariance. Since the velocity variances are diagnosed from COAMPS model output, thiscould be an artifact of this procedure. On the other hand, it could also be a manifest of asignificant wind direction shear through the jet. Another striking feature is that themagnitude of the scaled vertical velocity variances in many cases is unusually low, wellbelow the minimum value of the empirical function (Figure 23c). These points are primarilyfound above the katabatic jet. A functional relationship between the scaled vertical velocityvariance and stabili ty is also not as clear as for the two horizontal components.


35

10−3

10−2

10−1

100

101

102

103

0

1

2

3

4

5

6

7

8

9

10

z / LL

σ u / u L

z <= 0.5zjet

0.5z

jet < z <= 1.0z

jet1.0z

jet < z <= 1.5z

jet1.5z

jet < z <= 2.0z

jet2.0z

jet < z <= 5.0z

jet

(a)

10−3

10−2

10−1

100

101

102

103

0

1

2

3

4

5

6

7

8

9

10

z / LL

σ v / u L

z <= 0.5zjet

0.5z

jet < z <= 1.0z

jet1.0z

jet < z <= 1.5z

jet1.5z

jet < z <= 2.0z

jet2.0z

jet < z <= 5.0z

jet

(b)

10−3

10−2

10−1

100

101

102

103

0

1

2

3

4

5

6

7

8

9

10

z / LL

σ w /

u L

z <= 0.5zjet

0.5z

jet < z <= 1.0z

jet1.0z

jet < z <= 1.5z

jet1.5z

jet < z <= 2.0z

jet2.0z

jet < z <= 5.0z

jet

(c)

Figure 23. Modeled turbulence quantities over Breidamerkurjökull 00 to 24 UTC 7 July 1996, scaled in thesame way as in Figure 22; (a) along-flow component, (b) cross-flow component, and (c) vertical velocitycomponent. Solid lines in each panel are the empirical functions found in Paper III . The scaled variances arepartitioned into groups by normalized height according to legends.

STEFAN SÖDERBERG

36

From Figure 23a and 23b it is clear that the highest values of the scaled variances are foundnear the wind-speed maximum, where the stabili ty also is the largest. Above and below thejet, the magnitudes of the velocity variances and the stabili ty are more moderate. Since uL

appears both in the scaled standard deviation and in LL, there is a risk of self-correlationbetween the scaled standard deviations and z / LL (Mahrt et al. 1998). Moreover, Smeets etal. (2000) argued that near the wind-speed maximum, where the shear production ofturbulence should cease, uL becomes small and can therefore not represent a proper lengthscale while at the same time LL cannot be a proper length scale. To ill ustrate this, Smeets etal. (2000) plotted σw scaled with uL against z / zjet and found that the values becomeunusually large near the wind maximum. A comparable figure based on our results fromBreidamerkurjökull is shown in Figure 24a. It is immediately clear that there is a differencein scaling behavior between the observed katabatic flow over Pasterze glacier and thesimulated katabatic flow over Breidamerkurjökull . In contrast to the results in Smeets et al.(2000), where values become large due to that uL becomes much smaller than σw near thewind maximum, no such general tendency can be discerned in Figure 24a. In fact, in manycases our results show the opposite for z / zjet > 0.5, although it appears that σw in most casesdecrease at the same rate as uL when zjet is approached. Moreover, in Smeets et al. (2000) allthree velocity components varies at the same rate with normalized height, as implied by theconstant ratios σu /σw and σv /σw. Here σv actuall y becomes relatively large compared to uL

close to the wind maximum (Figure 24b). In addition, σv is reduced at a slower rate than σu

near the wind-speed maximum (not shown); this is another indication of directional shearthrough the jet as suggested by the unusually large values of the scaled cross-wind velocityvariance in Figure 23b.

From these observations we can only speculate as to why the three velocity variancesbehave in such a different manner in the katabatic flow above the two glaciers. One possibleexplanation may arise from differences in local flow features. Over Breidamerkurjökull , thekatabatic flow aligns with the glacier fall l ine on its way down towards the Atlantic Ocean(see Figure 14). In the lower part of the glacier, cross-slope advection can also be of

0.1 0.2 0.5 1 2 50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

z / zjet

σ w /

uL

(a)

0.1 0.2 0.5 1 2 50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

z / zjet

σ v / u

L

(b)

Figure 24. Normalized standard deviations of (a): the vertical component, and (b): the cross-flowcomponent, over Breidamerkurjökull, 00 to 24 UTC 7 July 1996, as a function of z / zjet.


37

importance for the momentum budget (Paper IV). The exact details of the katabatic flowover the Pasterze Glacier is presently not known except for that the fetch for theexperimental site which Smeets et al. (2000) collected data from, was relatively uniform.Differences in local flow characteristics between the two glaciers may therefore lead tosignificant differences in the contributions of non-local transport terms to the variancebudgets.

In COAMPS, second order moments are obtained from steady-state analytical expressionswhile TKE is a prognostic variable. In order to investigate possible non-local contributionsaffecting the form of the scaling functions, we will therefore have to study the TKE budget.In a coordinate system aligned with the mean flow u, the TKE (e) equation used inCOAMPS reads (Hodur 1987):

εθθ

−+∂∂−

∂∂−=

∂∂

∂∂−

∂∂+

∂∂

vv

e ''wg

z

v'w'v

z

u'w'u

z

eleS

zx

eu

t

e, (23)

where the two first terms on the LHS are the tendency and advection of TKE, respectively.The third term on the LHS is the turbulent diffusion of TKE, and represents both turbulentand pressure transport. As will become apparent later, this term is vital in the turbulenceclosure for studies of wind-speed jets. On the RHS in (23) the first and the second terms arethe shear production of TKE; the third term is the buoyancy production term; and the fourthterm is the dissipation term.

Over flat terrain, the stable TKE budget is essentially a balance between shear productionand dissipation, while buoyancy is a small sink term. Turbulence transport terms havetraditionally been neglected since they are much smaller than the other terms in the TKEbudget; this is also one of the assumptions in the local scaling theory (Niewstadt 1984). Inslope flow TKE budgets, the buoyancy term can also contribute to the balance. A balancebetween the production, dissipation and buoyancy terms was also what Smeets et al. (1999)found at the lower end of Breidamerkurjökull . This conclusion was, however, based onmeasurements during neutral or slightly stable conditions, and when the wind-speedmaximum was above the highest level of the mast. Of importance for the present thesis isthat turbulent transport may be significant in the region of the wind-speed maximum, whereturbulence production is small and a local minimum in TKE often occur (e.g., Arrit andPielke 1986; Horst and Doran 1988). Moreover, from measurements in katabatic flow overBreidamerkurjökull , van der Avoird and Duynkerke (1999) found that the contributions bynon-local sources and sinks in the TKE budget, increase with stabili ty.

Figure 25a shows the simulated TKE budget from the lower part of Breidamerkurjökull;corresponding profiles of downslope wind-speed (black solid), cross-slope wind (dashed),scalar wind-speed (gray solid), and potential temperature perturbation (dash-dotted) areshown in Figure 25b as a reference. The layer experiencing katabatic forcing (θ < 0) reachesup to z / zjet ≈ 3; note that even though the downslope wind-speed dominates the scalar wind-speed, there is a directional shear over the jet. In the region of the wind-speed maximum, alocal minimum is found in the TKE (not shown).

STEFAN SÖDERBERG

38

The profiles of shear (solid with circles), dissipation (solid with triangles) and buoyancy(thin solid) shown in Figure 25a are close to what we can expect to find in slope flows.Some distance away from the wind maximum, large magnitudes of the shear and dissipationterms are found, while distinct minima in both terms are centered at the wind maximum.The magnitude of the buoyancy term is smaller than the other two terms, but it is notnegligible, and acts as a sink in the TKE budget. The advection term in the TKE budget isoften neglected since its magnitude is small compared to the other terms (e.g., Stull 1988).According to our results, advection is a source term in the TKE budget below the windmaximum while it is a sink term above. However, the magnitude of the advection term isless than 5.10-5 m 2 s -3 and not included in Figure 25a. We therefore conclude that non-localcontributions to the TKE budget by advection are negligible in the simulated flow overBreidamerkurjökull .

A more likely non-local contributor to the TKE budget is the vertical mixing term (thicksolid). This is clearly il lustrated by the local maximum in the vertical mixing profile in theregion of the wind maximum. In fact, near the wind-speed maximum, local import of TKEis the main source in the TKE budget. These results also agree with the findings by Denby(1999) who used a more sophisticated turbulence closure than utili zed here, with prognosticequations for second-order moments. Moreover, assuming stationarity and horizontalhomogeneity, Smeets et al. (2000) found that turbulence and pressure transport terms importturbulence towards the wind maximum in the katabatic jet over the Pasterze glacier.Neglecting vertical transport of turbulence in katabatic flows is therefore not a validassumption; it is likely that this assumption is invalid also in studies of wind-speed jets ingeneral.

Recall that the largest discrepancies between the empirical scaling functions found in PaperIII , and the scaled velocity variances from Breidamerkurjökull, are found close to the wind-speed maximum. Since non-local contributions to the TKE budget are evident near thewind-speed maximum, it can very well be so, that the form of the scaling functions arecontrolled by non-local transport terms, in this case in the vertical, as hypothesized in PaperIII . This issue cannot be completely resolved in the present thesis but must be furtherinvestigated. A re-assessment of local similarity is required to investigate the dependency ofthe scaling functions on non-local properties of boundary layer flows.

−5 −4 −3 −2 −1 0 1 2 3 4 5

x 10−3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

TKE budget (m2 s−3)

z / z

jet

buoy shear diff vert mix

(a)

−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

(m s−1; oC)

z / z

jet

ud

vc

U θ

(b)

Figure 25. Normalized profiles from the model grid point closest to station A4 at 12 UTC, 7 July 1996 of(a): TKE budget, and (b): downslope wind component, cross-slope component, scalar wind speed, andpotential temperature deficit.


39

6. Concluding remarks and future outlook

The underlying goal for the studies included in the present thesis, has been to increase ourunderstanding of mesoscale flow and turbulence characteristics in complex atmosphericenvironments. To achieve this goal, the approach has been to combine “observations” from“the best out of two worlds” : measurements and numerical simulations. Admittedly, anumerical model is nothing more than just a model, i.e., a more or less crude simplificationof the real world. On the other hand, a model with a physically sound formulation isdynamically consistent. This implies that if a model is able to reproduce the general flowcharacteristics found in measurements then it is likely that these model results can also beused to draw general conclusions about physical properties and processes within the sametype of flow. This is of importance since measurements generally are sparse, in both timeand space. Combining measurements and numerical modeling may therefore lead to synergyeffects; basicall y that “1+1 > 2,” or, that measurements and numerical modeling combinedproduce greater results than either could separately.

In the present thesis, two types of mesoscale wind-speed jet and their effects on boundary-layer structure have been studied. The first is a coastal jet off the northern California coast,and the second is a katabatic jet over Vatnajökull , Iceland. Numerical modeling has been themain tool. However, observations have been used to verify that the numerical models arecapable of simulating the physical properties and processes within the studied flows and toensure a realistic behavior of the model results. Hence, observations constitute a basis onwhich the conclusions in this thesis rely. The flow response to terrain forcing, the transientbehavior in time and space, and agreement with simplified theoretical models have beenexamined for each of the jets. Moreover, the turbulence structure has been investigated inthese stably stratified boundary layers; local similarity scaling was applied to turbulencequantities. Among the findings in the thesis are:

• The simple shallow-water model provides a useful framework for analyzing high-velocity flows along mountainous coastlines, but for an unexpected reason. Wave energyis trapped in the capping inversion by the curvature of the wind-speed profile rather thanby an infinite stabili ty in the inversion separating two neutral layers, as assumed in thetheory. The observed supercritical flow response in coastal MABLs, downwind of capesand points with prominent terrain features is, however, probably a consequence of theblocking terrain, rather than the supercriticali ty of the flow. In the absence of blockingterrain, observations of steady-state supercritical flow are not likely.

• A reasonable agreement between simulated katabatic flow characteristics and thosepredicted by an analytical model is found. Nevertheless, some discrepancies areapparent, primarily in the lower part of the glacier. It is hypothesized that these are dueto non-local effects neglected in the theory, such as surface inhomogeneity and slopegeometry.

• A possible explanation for the different forms of the local similarity scaling functionsbetween different studies, may be that non-local transports terms significantlycontributes to the velocity variance budgets but not to the stress. Since non-localprocesses may differ significantly between different data sets, the scaling functions willalso differ between studies. This issue awaits analysis of a more extensive data set,covering a wide range of stabiliti es and flow types, to be settled.

STEFAN SÖDERBERG

40

The results listed above all are examples of how modeling efforts can shed new light onobserved flow and turbulence characteristics: the impact of the local terrain at CapeMendocino on the MABL properties was clearly revealed in the numerical simulationsperformed here; possible effects of non-local processes, often neglected in simplifiedtheoretical models, were also ill ustrated. Important to remember though, is that a numericalmodel alone cannot shed new light on atmospheric processes, which are poorly understoodon a more basic level.

The general trend in numerical modeling today is that we are steadily moving towardshigher horizontal and vertical resolutions, primarily as a consequence of the increasingcomputer capacity available to the community. This gives us the opportunity to studyatmospheric processes on a finer and finer scale. However, although the resolution innumerical models steadily increases, we will still need parameterizations of physicalprocesses in the atmosphere. Even in large-eddy-simulations numerous sub-grid scaleprocesses must be parameterized; for computational reasons, direct numerical simulationswill li kely never be used in numerical weather forecasting. On the other hand, in the earlystages of the ongoing computer-era, Tomas Watson, chairman of IBM said in 1943: “ I thinkthere is a world market for maybe five computers.” Another well -known quote from 1981 is:“640K of memory should be enough for anybody.” The (in) famous Bill Gates howeverstates, “ I've said some stupid things and some wrong things, but not that” and claims that hewas misquoted.

Nevertheless, an increased resolution in the numerical models also implies that non-localprocesses become more important. Including effects like these in parameterizations ofatmospheric processes is therefore one upcoming task for the community if we are toincrease the skill in regional weather predictions. To develop physically soundparameterizations is probably even more important when they are to be applied in generalcirculation models for studies of our present and future climate.


41

Acknowledgements

So, finall y the day has come when it is time to present what I've been up to for the lastcouple of years. As always when you are about to wrap things up and are just a littl e bitshort of time, you tend to wonder how all those days just went by. Nevertheless, here I amwith a thesis in my hand and for this, I owe a number of people a lot of gratitude. Some willspecifically be mentioned here, but there is not room to include all of you, so you will haveto trust me when I say that I have you in my mind.

I'm grateful to my supervisors Michael Tjernström and Branko Grisogono. Without yoursupport, all knowledge you've been willing to share, and enthusiasm, it would have been somuch harder to complete this thesis. Except for being excellent supervisors, you are also tworeally nice guys and I want to thank Michael and his family, and Branko for all nice dinnerparties and pastries. I also have to give Michael some extra credit for taking me on as astudent. The opportunities you have given me to attend conferences and present my workare also highly appreciated; I have learned a lot from these trips.

Another person that has been (still is, and will be in the future) invaluable to me is my wifeMalin. Taking care of our son Martin (who's also invaluable), yourself, and on top of thisme, the last couple of months has been an achievement few people could have managed.Without you, life just wouldn't be the same. It is hard to find words for how nice it will bewhen this thesis finally has been defended, and I can spend more time with the both of you.

However, we have to wait a few more days until we can enjoy some “ lazy days” together, atleast lazy relative to today, so here are some more people who work or have been working atMISU over the years, that I want to thank. My one and only roommate Måns Manilow, alsoknown as Barry Håkansson, did his best teaching me all he knows about "jazzträsket". Tohis despair, I still think Neil Young has written some really nice songs. Nevertheless,sharing office with you is a privilege to anyone; you are simply one of the nicest and kindestpersons that I've ever met! Following in your footsteps, I spent almost two months in theArctic Ocean during the summer of 2001. Special thanks goes to Caroline Leck, who gaveme the opportunity to go there, transformed into a chemist. Patrick Samuelsson isacknowledged for being such a nice guy and an excellent traveling companion; Mark Zagaris thanked for the same reasons. Another person who deserves a special recognition is EvaTiberg, without you I would have been totall y lost some days! Oskar Parmhed is thanked fora fruitful collaboration; working together is more fun than sitting alone “ in the darkness.”All fellow Ph.D. students are also thanked for various social events making life at and offwork more pleasant.

I have met many inspiring people during my studies. In particular I want to mention SteveBurk, Willi am Thompson, Tracy Haack, Ola Persson, Carmen Nappo, and Ian Brooks.Thanks a lot for being such nice guys whenever and wherever we have met. Douglas Adamsand Gary Larson are also acknowledged for their good sense of humor, and so is Leif Enger,one of Uppsalas most talented chefs.

Finally, I want to thank all my friends and my family for support and distraction from workon occasions when that have been called for. To all of you, be prepared for here I come,soon I will be in a place near you for a social visit!! !

STEFAN SÖDERBERG

42

References

Al-Jiboori, M. H., Y. Xu, and Y. Qian, 2002: Local similarity relationships in the urbanboundary layer. Bound.-Layer Meteor., 102, 63-82.

Andrén, A., 1990: Evaluation of a turbulence closure scheme suitable for air-pollutionapplications. J. Appl. Meteor., 29, 224-239.

Arritt, R., and Pielke, R., 1986: Interactions of nocturnal slope flows with ambient winds.Bound.-Layer Meteor., 37, 183–195.

Beardsley, R. C., C. E. Dorman, C. A. Friehe, L. K. Rosenfeld, and C. D. Winant, 1987:Local atmospheric forcing during the coastal ocean dynamics experiment. 1. Adescription of the marine boundary layer and atmospheric conditions over a northernCalifornia upwelling region. J. Geophys. Res., 92, 1467-1488.

Brooks, I. M., and D. P. Rogers, 2000: Aircraft observations of the mean and turbulentstructure of a shallow boundary layer over the Persian Gulf. Bound.-Layer Meteor., 95,189-210.

Brost, R. A., H. Lenshow, and J. C. Wyngaard, 1982: Marine stratocumulus layers. Part I:Mean conditions. J. Atmos. Sci., 39, 800-817.

Burk, S. D., and W. T. Thompson, 1996: The summertime low-level jet and marineboundary-layer structure along the California coast. Mon.Wea. Rev., 124, 668-686.

Burk, S. D., T. Haack, and R. M. Samelson, 1999: Mesoscale simulation of supercritical,subcritical and transcritical flow along coastal topography. J. Atmos. Sci., 56, 2780-2795.

Denby, B., 1999: Second-order modell ing of turbulence in katabatic flows. Bound.-LayerMeteor., 92, 67-100.

Dorman, C. E., 1985: Evidence of Kelvin waves in California’s marine layer and relatededdy generation. Mon. Wea. Rev., 113, 827–839.

Dorman, C. E., T. Holt, D. P. Rogers, and K. Edwards, 2000: Large-Scale Structure of theJune–July 1996 Marine Boundary Layer along Cali fornia and Oregon. Mon. Wea. Rev.,128, 1632-1652.

Edwards, K. A., A. M. Rogerson, C. D. Winant, and D. P. Rogers, 2001: Adjustment of themarine atmospheric boundary layer to a coastal cape. J. Atmos. Sci., 58, 1511-1528.

Enger, L., 1990: Simulation of dispersion in moderately complex terrain - Part A. The fluiddynamic model. Atmos. Environ., 24A, 2431-2446.

Enger, L., and B. Grisogono, 1998: The response of Bora-type flow to sea-surfacetemperature, Quart. J. Roy. Meteor. Soc., 124, 1227-1244.

Greuell , J. W., M. R. van den Broeke, W. Knap, C. Reijmer, P. Smeets, and I. Struijk, 1994:PASTEX: A Glacio-Meteorological Experiment on the Pasterze (Austria). Field Report,Institute for Marine and Atmospheric Research, Utrecht University, 34 pp.

Grisogono, B., and M. Tjernström, 1996: Thermal mesoscale circulations on the Balticcoast. 2. Perturbation of surface parameters, J. Geophys. Res., 101, 18999-19012.

Harshvardhan, R. Davies, D. Randall , and T. Corsetti, 1987: A fast radiationparameterization for atmospheric circulation models. J. Geophys. Res., 92, 1009-1016.

Hodur, R. M., 1997: The Naval Research Laboratory’s coupled ocean/atmospheremesoscale prediction system (COAMPS). Mon. Wea. Rev., 125, 1414-1430.


43

Horst, T. W., and J. C. Doran, 1988: The turbulence structure of nocturnal slope flow. J.Atmos. Sci., 45, 605-616.

Ippen, A. T., 1951: Mechanics of supercritical flow. Trans. Amer. Soc. Civil . Eng., 166,268-295.

Kain, J.S. and Fritsch J. M., 1990: A one-dimensional entraining/detraining plume modeland its application in convective parameterization. J. Atmos. Sci., 47, 2784-2802.

Kaltenböck, R. and Obleitner, F., 1999: On a low cloud phenomenon at theBreidamerkurjökull glacier, Iceland. Bound.-Layer Meteor., 92, 145-162.

King, J., 1990: Some measurements of turbulence over an antarctic ice shelf. Quart. J. Roy.Meteor. Soc., 116, 379-400.

Klemp, J., R. Rotunno, and W. Skamarock, 1997: On the propagation of internal bores. J.Fluid Mech., 331, 81–106.

Lenschow, D. H., C. J. Zhu, and B. B. Stankov, 1988: The stably stratified boundary layerover the great plains I: Mean and turbulence structure. Bound.-Layer Meteorol., 42,95-121.

Mahrt, L., 1982: Momentum balance of gravity flows. J. Atmos. Sci., 39, 2701-2711.Mahrt, L., J. Sun, W. Blumen, T. Delany, and S. Oncley, 1998: Nocturnal boundary-layer

regimes. Bound.-Layer Meteor., 88, 255–278.Mellor, G. L., and T. Yamada, 1982: Development of a closure model of geophysical flows.

Reviews of Geophysics and Space Physics, 20, 851-875.Nappo, C. J., 2002: An Introduction to Atmospheric Gravity Waves. Academic Press, San

Diego, 276 pp.Nappo, C. J., and P.-E. Johansson, 1999: Summary of the Lövånger international workshop

on turbulence and diffusion in the stable planetary boundary layer. Bound.-LayerMeteor., 90, 345-374.

Nieuwstadt, F. T. M., 1984: The turbulent structure of the stable, nocturnal boundary layer. J.Atmos. Sci., 41, 2202-2216.

Nuss, W. A., J. M. Bane, W. T. Thompson, T. Holt, C. E. Dorman, F. M. Ralph, R.Rotunno, J. B. Klemp, W. C. Skamarock, R. M. Samelson, A. M. Rogerson, C. Reason,and P. Jackson, 2000: Coastally trapped wind reversals: Progress toward understanding.Bull . Amer. Meteor. Soc., 81, 719-743.

Oerlemans, J., 2001: Glaciers and Climate Change. A. A. Balkema publishers, TheNetherlands.

Oerlemans, J. and Grisogono, B., 2002: Glacier winds and parameterisation of the relatedsurface heat fluxes. Tellus, 54A, 440-452.

Oerlemans, J., Björnsson, H., Kuhn, F., Obleitner, F., Palson, F., Smeets, C. J. P. P., Vugts,H. F., and De Wolde, J., 1999: Glacio-meteorological envestigations on Vatnajökull ,Iceland, summer 1996: An overview. Bound.-Layer Meteor., 92, 3-26.

Ólafsson, H, and P. Bougeault, 1996: Nonlinear flow past an elli ptic mountain ridge. J.Atmos. Sci., 53, 2465-2489.

Pahlow, M., M. B. Palange, and F. Porté-Agel, 2001: On Monin-Obukhov similarity in thestable atmospheric boundary layer. Bound.-Layer Meteor., 99, 225-248.

Parmhed, O., J. Oerlemans, and B. Grisogono, 2004: Describing surface-fluxes in katabaticflow on Breidamerkurjökull , Iceland. Quart. J. Roy. Meteor. Soc., in press.

STEFAN SÖDERBERG

44

Poulos G. S., W. Blumen, D. C. Fritts, J. K. Lundquist, J, Sun, S. P. Burns, C. Nappo, R.Banta, R. Newsom, J. Cuxart, E. Terradellas, B. Balsley, and M. Jensen, 2002: CASES-99: A comprehensive investigation of the stable nocturnal boundary layer. Bull . Amer.Meteor. Soc., 83, 555-581.

Prandtl, L., 1942: Führer durch die Strömungslehre. Vieweg und Sohn, Braunschweig,Germany, 648 pp.

Ralph, F. M., P. J. Neiman, P. O. G. Persson, J. M. Bane, M. L. Cancillo, J. M. Wilczak, andW. A. Nuss, 2000: Kelvin waves and internal bores in the marine boundary layerinversion and their relationship to coastally trapped wind reversals. Mon. Wea. Rev., 128,283–300.

Rogers, D. P., C. E. Dorman, K. Edwards, I. Brooks, K. Melvill e, S. D. Burk, W. T.Thompson, T. Holt, L. Ström, M. Tjernström, B. Grisogono, J. M. Bane, W. Nuss, B.Morley, and A. Schanot, 1998: Highlights of Coastal Waves 1996. Bull . Amer. Meteor.Soc., 79, 1307-1326.

Rogerson, A. M., 1999: Transcritical flows in the coastal marine atmospheric boundarylayer. J. Atmos. Sci., 56, 2761-2779.

Rutledge, S. A. and P. V. Hobbs, 1983: The mesoscale and microscale structure andorganization of clouds and precipitation in midlatitude cyclones. Part VIII : A model forthe “Seeder-Feeder” process in warm-frontal rainbands. J. Atmos. Sci., 40, 1185-1206.

Samelson, R. M., 1992: Supercritical marine-layer flow along a smoothly varying coastline.J. Atmos. Sci., 49, 1571-1584.

Samelson, R. M., and S. J. Lentz, 1994: The horizontal the marine atmospheric boundary. J.Atmos. Sci., 51, 3745–3757.

Shao, Y., and Hacker, J. M., 1990: Local similarity relationships in a horizontallyinhomogeneous boundary layer. Bound.-Layer Meteor., 52, 17-40.

Smedman, A-S., H. Bergström, and U. Högström, 1995: Spectra, variances, and lengthscales in a marine stable boundary layer dominated by a low level jet. Bound.-LayerMeteor., 76, 211-232.

Smeets, C. J. P. P., P. G. Duynkerke, and H. F. Vugts, 1998: Turbulence characteristics ofthe stable boundary layer over a mid-latitude glacier. Part I: A combination of catabaticand large-scale forcing. Bound.-Layer Meteor., 87, 117–145.

Smeets, C. J. P. P., P. G. Duynkerke, and H. F. Vugts, 1999: Observed wind profiles andturbulence fluxes over an ice surface with changing surface roughness. Bound.-LayerMeteor., 92, 101–123.

Smeets, C. J. P. P., P. G. Duynkerke, and H. F. Vugts, 2000: Turbulence characteristics ofthe stable boundary layer over a mid-latitude glacier. Part II : Pure katabatic forcingconditions. Bound.-Layer Meteor., 97, 73-107.

Sorbjan, Z., 1986: On similarity in the atmospheric boundary layer. Bound.-Layer Meteor.,34, 377-397.

Sorbjan, Z., 1987: An examination of the local similarity theory in the stably stratifiedboundary layer. Bound.-Layer Meteor., 38, 63-71.

Stull , R. B., 1988: An Introduction to Boundary Layer Meteorology. Kluwer academicpublishers, Dordrecht, The Netherlands, 666 pp.


45

Ström, L., M. Tjernström and D. P. Rogers, 2001: Observed dynamics of coastal flow atCape Mendocino during Coastal Waves 1996. J. Atmos. Sci., 58, 953-977.

Tjernström, M., 1987a: A study of flow over complex terrain using a three-dimensionalmodel. A preliminary model evaluation focusing on stratus and fog. Ann. Geophys., 88,469-486.

Tjernström, M., 1987b: A three-dimensional meso-γ-model for studies of stratiformboundary layer clouds: A model description. Rep. 85, Department of Meteorology,Uppsala University, Uppsala, Sweden, 44 pp.

Tjernström, M., 1999: The sensitivity of supercritical atmospheric boundary-layer flowalong a coastal mountain barrier. Tellus, 51A, 880-901.

Tjernström, M., and B. Grisogono, 1996: Thermal mesoscale circulations on the Balticcoast. 1. A numerical case study. J. Geophys. Res., 101, D14, 18979-18997.

Tjernström, M., and B. Grisogono, 2000: Simulations of supercritical flow around pointsand capes in a coastal atmosphere. J. Atmos. Sci., 57, 108-135.

van der Avoird, E., and P. G. Duynkerke, 1999: Turbulence in a katabatic flow. Does itresemble turbulence in stable boundary layers over flat surfaces? Bound.-Layer Meteor.,92, 36-66.

Winant, C. D., C. E. Dorman, C. A. Friehe, and R. C. Beardsley, 1988: The marine layer offnorthern California - an example of supercritical channel flow. J. Atmos. Sci., 45,3588-3605.

Zemba, J., and C.A. Friehe, 1987: The marine atmospheric boundary-layer jet in the coastalocean dynamics experiment. J. Geophys. Res., 92, 1489-1496.

1)737'%0) (=2%1-'7 %2( &392(%6= 0%=)6 03; 0):)0...

Documents

Transcript of 1)737'%0) (=2%1-'7 %2( &392(%6= 0%=)6 03; 0):)0...